Bring 4 cups of water to a boil in a large pot over high heat.
Add 1½ teaspoons salt, the jumbo pasta shells, and the chopped broccoli to the boiling water.
Cook, stirring occasionally, for about 8 minutes until pasta is al dente and broccoli is tender; do not drain the pot.
Reduce heat to medium-low and stir in 1 cup heavy cream or whole milk.
Add shredded cheddar, shredded provolone, and ricotta, stirring until the cheeses melt and form a creamy sauce.
Stir in the baby spinach, garlic powder, onion powder, paprika, and chipotle chili powder until the spinach wilts and ingredients are evenly combined.
Remove the pot from the heat and fold in the chopped basil and lemon zest. Taste and season with salt and black pepper as needed.
If the sauce is too thick, thin with up to an additional ¼ cup milk until you reach the desired consistency.
Divide the pasta and broccoli between bowls and serve immediately, topping with extra basil or lemon zest if desired.