Fill a large pot with water, add salt, and bring to a boil. Cook rigatoni pasta according to package instructions until al dente, about 10-12 minutes. Reserve 1 cup pasta water, then drain pasta and set aside.
Heat olive oil in a large skillet over medium heat. Add diced onion and cook until softened and translucent, about 3-4 minutes. Stir in minced garlic and cook another 30 seconds until fragrant.
Add sliced mushrooms to the skillet and cook, stirring occasionally, until golden brown and moisture evaporates, about 6-8 minutes.
Add fresh spinach to the skillet and cook until just wilted, about 1-2 minutes.
Pour in heavy cream and stir to combine. Simmer gently for 2-3 minutes until sauce thickens slightly. Stir in grated Parmesan cheese and season with salt and pepper. Add reserved pasta water if sauce is too thick.
Add cooked rigatoni pasta to the skillet with sauce. Toss over low heat to coat pasta evenly and warm through. Adjust seasoning if needed.
Remove skillet from heat. Garnish with chopped fresh parsley and serve immediately with extra Parmesan if desired.