Heat the butter in the Instant Pot on 'Sauté' mode. Add in the onion and garlic and cook until soft, about 3 to 4 minutes.: As the butter melts, you will hear a gentle sizzle and smell a warm, inviting aroma that signals the pan is ready. This step develops a flavor foundation by softening the fat and creating a surface for the onion and garlic to release their aromatics. A common mistake is using too high a heat which causes the butter to brown or burn, introducing bitter notes; keep the pot on a moderate sauté setting and watch for a light foam and warm nutty scent.
Add in the broccoli, chicken broth and carrot.: You will notice the onion becoming translucent and the kitchen filling with a sweet, savory scent; the garlic will become fragrant but should not brown. Softening these aromatics mellows sharp edges and creates sweetness that deepens the soup's profile. Avoid rushing this step, because undercooked onion can leave a raw, harsh edge; if you see browning, lower the heat and stir more frequently.
Cover and set to 'Sealing'. Cook on manual high pressure for 10 minutes. Do an instant steam release.: When the broccoli and carrot join the pot, the color contrast is immediate, and the broth will glisten around the vegetables. Adding the chicken broth deglazes the base and captures any caramelized bits from the sauté, enriching flavor. Make sure the vegetables are submerged enough for even pressure cooking; a common oversight is overcrowding which can lead to uneven tenderness.
In a small bowl, whisk the cornstarch with 1/4 cup of warm water.: The pot will build pressure and then cook the vegetables until tender yet still vibrant. During sealing you may hear clicks and hisses, which is normal as steam builds. This pressurized environment gently breaks down the vegetables, creating body in the soup. Avoid opening the valve early unless the recipe calls for it, because premature release can result in undercooked pieces.
While stirring constantly, whisk the mixture back into the soup. Turn to 'Sauté' mode and cook until thickened, about 2 to 4 minutes.: As you vent, you will see a plume of steam and hear a rush; this rapid release stops cooking quickly so textures remain controlled. This technique prevents the broccoli from over softening into a mushy mass. A common mistake is placing your hand over the valve; always use a utensil and keep your face and hands away from the steam stream.
Turn off the Instant Pot and stir in the cheese a little bit at a time until fully melted.: The slurry should be smooth and glossy with no visible clumps, and the warm water helps it dissolve evenly. This activation step readies the cornstarch to thicken without leaving gritty pockets. If you see lumps, push the mixture through a small sieve or whisk vigorously; adding it lumpy will create uneven texture when incorporated.
Stir in the cream and season to taste with salt: As the slurry hits the hot liquid you will hear a soft bubbling and notice the soup beginning to coat the back of a spoon, indicating proper thickening. Constant stirring prevents localized gelatinization that causes lumps, and finishing on sauté evaporates excess liquid so the texture firms up. A trap here is turning the heat too high which can break down the cream; keep a moderate sauté and watch for a glossy sheen.
Turn off the Instant Pot and stir in the cheese a little bit at a time until fully melted: As you add the cheddar in small handfuls, it will melt into smooth ribbons that deepen the soup's color and create a luxuriously creamy body. Adding cheese off heat or on minimal residual warmth prevents separation and graininess. A common mistake is dumping all the cheddar in at once which can lead to clumping and an oily finish; take your time and stir continuously.
Stir in the cream and season to taste with salt: The whipping cream will meld into the surface, smoothing any sharpness and giving the soup a rich mouthfeel that clings to the spoon. Taste carefully because the chicken broth and cheddar already contain salt; add small increments of sea salt until flavors brighten without becoming salty. Over seasoning is easy to do here, so pause and taste after each tiny addition.