Bring 4 cups of water to a rolling boil in a large pot over high heat.
Add 1 1/2 teaspoons salt, the jumbo pasta shells, and the chopped broccoli to the boiling water; stir, then cook uncovered, stirring occasionally, for about 8 minutes.
Without draining, reduce heat to medium and stir in the heavy cream or milk
Add the shredded cheddar, shredded provolone, ricotta, baby spinach, garlic powder, onion powder, paprika, and chipotle chili powder; stir until the cheeses melt and the sauce becomes creamy.
Remove the pot from the heat, then stir in the chopped basil and lemon zest; taste and season with additional salt and black pepper as desired.
If the sauce is too thick, thin it with up to 1/4 cup more 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.