Bring 4 cups of water to a boil in a large pot over high heat.
Add 1½ teaspoons salt, the jumbo pasta shells, and chopped broccoli to the boiling water.
Cook, stirring occasionally, for 8 minutes; do not drain the water.
Reduce heat to medium, then stir in 1 cup of heavy cream or whole milk.
Add the shredded cheddar, shredded provolone, and ricotta; stir 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 everything is combined.
Remove the pot from the heat and fold in the chopped fresh basil and 1–2 tablespoons lemon zest. Taste and season with salt and black pepper.
If the sauce is too thick, add up to ¼ cup additional milk to thin to your desired consistency.
Divide the pasta and broccoli among bowls and serve topped with extra basil and lemon zest if desired.
