Preheat the oven to 400 degrees F. Place the broccoli pieces on a large baking sheet. Drizzle with olive oil and lemon juice. Add the garlic and toss broccoli until well coated. Season with salt and pepper, to taste. Place baking sheet in the oven and roast for 20-25 minutes, stirring once. Remove broccoli when it is crisp and slightly charred. Set aside.: The scent of caramelizing vegetables is one of the best signals that roasting is working, with notes of sweetened green and a faint smokiness when edges char; you should hear a soft sizzle when the baking sheet first goes in, and the florets will visibly darken at the tips. Roasting concentrates flavor by driving off water and allowing natural sugars to caramelize, which is why I prefer a hot oven so the surface browns quickly while the interior stays tender. A common mistake is overcrowding the pan, which steams the broccoli instead of roasting it; give each piece space so air can circulate. When stirring once midway, use a metal spatula to turn pieces that are browning too fast so nothing burns. Visual cues to look for are lightly crisped edges and a bright, softened green in the stems. If you accidentally under roast them, return the pan for a few more minutes rather than increasing the temperature drastically, which can scorch the garlic.
Meanwhile, bring a large pot of salted water to a boil. Cook tortellini according to package instructions. When cooked, drain, but reserve 1/2 cup of the pasta water. Set the water and tortellini aside.: You will notice the water smell change as it reaches a rolling boil, and the salted water seasons the tortellini from the inside out; the pasta should float or feel tender but still offer a slight bite when you taste it. Reserving some of the starchy cooking water is key because it binds the sauce and helps it cling to the cheese tortellini . A frequent error is draining everything and throwing away the water, which can make the final dish dry. If your tortellini seems sticky after draining, toss it with a drizzle of olive oil to keep pieces separate before adding to the sauce. Use the reserved water to loosen the sauce slowly, rather than adding all at once, so you control the consistency.
Put the pot back on the stove and melt the butter over medium heat. Add the shallot, garlic, crushed red pepper, and spinach and cook until spinach is wilted, about 3 minutes. Add the lemon zest and stir.: When the butter melts it will foam slightly and release nutty aromas; the softened shallot should become translucent and sweet, while the minced garlic will perfume the pan without browning. The sound will shift from a gentle simmer to a softer sizzle as the spinach collapses, turning vivid green before it wilts. This short cook time preserves the fresh notes and prevents the greens from becoming mushy. Overcooking at this stage dulls the brightness, so watch closely and stir frequently. If the heat is too high the garlic can burn, creating a bitter edge; reduce the heat if you see browning. Adding the lemon zest at the end preserves its aromatic oils, giving a fragrant lift rather than a cooked citrus flavor.
Turn the heat to low and add the cooked tortellini and roasted broccoli to the pot. Stir in the reserved pasta water and lemon juice. Cook on low until tortellini is warm, about two minutes. Sprinkle Parmesan cheese over the tortellini and season with salt and pepper, to taste. Serve warm.: At this stage you will feel the warmth spread through the pot and hear a gentle simmer as the reserved starchy water binds with the butter to form a light coating; the aroma will be a mix of tangy lemon , nutty Parmesan cheese , and roasted broccoli . The reason for cooking on low is to avoid breaking the tortellini and to let the flavors marry gently so the cheese melts into a silky finish. One common slip is overheating which can cause the tortellini to burst or the sauce to separate; keep the heat minimal and stir carefully. If the sauce seems too thin, let it reduce for a minute or two, or if it is too thick, add a splash more reserved pasta water. Final seasoning is subjective so taste before serving, aiming for a balance of salt, pepper, and lemon brightness. A final flourish of extra Parmesan cheese on top adds umami and a pleasing grainy texture on the tongue.