Cook the pasta according to package directions. Reserve 1 cup of the cooking liquid before draining.: The kitchen fills with the comforting scent of boiling starch as the pasta cooks, and listening for the subtle change in bubbling helps you gauge doneness. When it reaches the point where the center has a tiny firm core, it will finish cooking in the pan with the vegetables and sauce, so undercook by a touch if you prefer a firmer bite. Reserve a cup of that starchy cooking water, because its slightly thickened texture is what will bind the lemon and parmesan cheese to the pasta , creating a glossy coating. A common mistake is draining everything and tossing immediately, which leaves the dish dry. If the pasta seems too sticky while draining, give it a quick shake but do not rinse, rinsing washes away the starch you need for the sauce.
While the pasta is cooking, heat the oil in a saute pan over medium heat. Add the onions and saute until soft, about 3 minutes. Add the garlic, carrots, broccoli, and peas and saute another 3-5 minutes. Add the spinach and cook for 1 minute more.: As the oil warms, it becomes a thin mirror in the pan that quickly carries heat and flavor, and the chopped onion will begin to release sweet, savory aromas as it softens. You will hear a gentle sizzle when the vegetables hit the pan, and that sound signals flavor development through gentle caramelization. Adding minced garlic after the onion prevents burning, and once the shredded carrots , chopped broccoli , and frozen peas join the party the mixture will steam slightly, softening while maintaining bite. When you toss in the packed fresh spinach , it will quickly wilt, collapsing into a vivid green softness. The key here is to avoid high heat that scorches the edges, and instead cook over medium so the vegetables become tender without losing color. A frequent misstep is overcooking the vegetables into mush, so stay attentive and sample a piece to check texture.
Add the vegetables to the cooked pasta, toss with the lemon juice, parmesan cheese and reserved pasta water to combine thoroughly.: As you fold the warm vegetables into the drained pasta , you will notice steam rising and a burst of citrus aroma when the lemon juice hits the hot starch. Begin adding the reserved cooking water a little at a time, and watch the sauce transform from thin to silky, coating each curl and hollow of the pasta . The grated parmesan cheese will melt into this emulsion, yielding a creamy mouthfeel without any cream. Taste as you go to adjust the amount of lemon and water, because acidity and saltiness balance differently on every batch of cheese and pasta. If the mixture seems thin, let it sit off heat for a minute to thicken slightly; if it is too thick, add another splash of the reserved water. A typical mistake is dumping all the liquid at once, which can make the sauce watery instead of luxuriously glossy. Finish by giving a final toss to ensure even distribution of flavors, and serve while warm so the textures remain distinct and vibrant.