Bring 4 quarts of water to a boil in a large pot. Swirl in the 3 tablespoons table salt.
Dump in the 12 ounces rigatoni and cook according to the package directions. Drain, reserving 1/2 cup of the pasta water.
While the pasta cooks, stir together the 1 cup whole milk ricotta, 1/2 teaspoon lemon zest, 3/4 teaspoon of the salt, and the 1/4 teaspoon freshly ground black pepper in a small bowl.
In a large skillet over medium heat, warm the 2 tablespoons extra-virgin olive oil. Add the 6 garlic cloves and cook until fragrant, 1 minute. Stir in the 1/2 cup sun-dried tomatoes in oil, 2 generous pinches red pepper flakes, the 5 cups fresh baby spinach, and the remaining 1/4 teaspoon salt. Cook until the spinach is wilted, 3 to 4 minutes.
Dump the cooked pasta into the skillet and toss for 2 minutes to warm through.
Add the ricotta mixture, along with 2 tablespoons of the reserved pasta water. Stir until the pasta is well coated and creamy. (If the sauce is too thick, add more water, 1 tablespoon at a time.) Take a taste and season with more salt and pepper if needed.
Transfer the pasta to a warm serving bowl and serve immediately with grated Parmesan cheese on the side.