Pull the dill fronds from the stems; reserve 1/2 cup of the fronds for garnish.: The scent of fresh dill should be immediate and herbaceous when you separate fronds from stems, a green perfume that hints at the bright finish to come. Work over a bowl to catch bits and keep the kitchen tidy, and use your fingers to gently strip rather than chop right away, preserving delicate leaf texture. Avoid bruising the fronds which can make them taste slightly bitter. If the dill seems limp, a quick rinse and dry will revive it, but be sure the leaves are mostly dry so they don't water down the garnish appearance.
In a pot, combine the stems, chicken thighs and rice with the chicken broth and bring to a boil over high heat.: When the pot first comes up to a boil you will notice vigorous bubbling and a savory aroma as the chicken broth and stems release flavors into the liquid. The rolling boil helps extract collagen and taste from the chicken and stems, which will deepen the broth. Keep an eye on the pot so it doesn't foam over, and stir gently to distribute the rice . A common error is boiling too long at high heat, which can make the chicken tough later, so this initial high heat is brief and purposeful.
Lower the heat to medium-low and stir. Cover and cook the chicken until tender, 25 minutes.: As you reduce to a gentle simmer the surface will show slow, steady ripples and the aroma will intensify into a warm, savory note. Covered, the steam cooks the chicken through while the rice absorbs liquid; the texture should be tender not falling apart. Check for a gentle simmer rather than a boil, because agitation can break grains and make the broth cloudy. Avoid lifting the lid too often, which can extend cooking time and cool the pot unnecessarily.
Use a slotted spoon to remove the chicken and stems from the broth. Discard the stems and transfer the chicken to a plate then shred with 2 forks.: Removing solids brightens visual clarity and concentrates the broth's flavor. When you transfer the hot chicken to a plate and shred with forks, the meat should pull apart easily, yielding moist ribbons that will later meld with the egg lemon mixture. If the meat resists shredding, it may need a few more minutes; shredding while the meat is very hot makes it easier. Discarding the stems prevents woody bitterness in the finished soup.
Meanwhile, increase the heat to medium-high and bring the stock up to an active simmer.: Raising the heat restores movement to the pot, and you will see more pronounced bubbles rising to the surface, which is ideal for tempering because you want hot, not boiling, broth. The simmer concentrates flavors and slightly reduces volume, intensifying the soup. Be vigilant now, because if the broth boils aggressively when you add the egg mixture it can cook the eggs into curds. Keep the simmer steady and controlled to avoid this.
In a large heatproof bowl, vigorously whisk the eggs until frothy. Add 1/4 cup lemon juice and mix to incorporate.: The eggs should become pale and airy as you whisk, taking on a light froth that helps them blend smoothly into the hot liquid later. When you add the lemon juice , the mixture will smell bright and tangy, a signal that the soup will finish with lively acidity. Vigorous whisking helps incorporate air, which stabilizes the egg when tempered. A frequent mistake is underwhisking, which can increase the chance of the eggs separating when introduced to heat.
While you whisk the eggs, gradually drizzle in 1 ladleful (about 1 cup) of the broth (it’s OK if some grains of rice tag along) and mix until fully combined.: As warm broth meets the egg lemon mixture you should notice steam and a gentle increase in temperature without any curdling. The gradual drizzle is crucial to raise the eggs to broth temperature safely, creating a glossy emulsion. If you pour too quickly the eggs can scramble, producing grainy bits, so patience here prevents that outcome. If a few rice grains enter the bowl, they will soften the mixture and are harmless, but avoid transferring large amounts of solids which can cool the ladle and interrupt tempering.
Pour the lemon-egg mixture into the pot with the broth, immediately remove from the heat, and stir in the shredded chicken. Taste and add more lemon juice to taste.: Right after pouring, remove the pot from direct heat to keep the residual warmth from overcooking the eggs, and stir gently so the texture turns silky and smooth without separating. You should hear a barely audible simmer and see the broth thicken slightly, taking on a satiny sheen as the emulsion sets. Adding the shredded chicken now warms the meat gently without drying it. A key trap is returning the pot to high heat too soon, which will cause curdling, so keep it off the burner while you finish seasoning.
Garnish with a generous amount of fresh dill, black pepper and a drizzle of olive oil.: At this point the aroma should be bright lemon balanced by savory broth and tender chicken . Taste carefully and add incremental amounts of lemon juice until you reach a lively but balanced acidity that complements the eggs and broth. I often add a small squeeze and then wait a minute before reassessing, because the flavors settle as the bowl cools slightly. Over-acidifying is the most common misstep, so adjust slowly and with restraint.
Garnish with a generous amount of fresh dill black pepper and a drizzle of olive oil.: The final assembly adds visual contrast and aromatic lift, with the chopped dill brightening each spoonful and the cracked black pepper giving a gentle bite. A light drizzle of olive oil adds sheen and an extra layer of flavor that rounds the bowl. Serve immediately so the garnish retains its texture, because letting the herbs sit in hot liquid will diminish their crispness. If the soup sits too long, reheat gently while stirring to maintain the silky consistency.