In a large pot, bring salted water to a boil. Add the pasta and cook according to package instructions until al dente. Reserve 1/2 cup of pasta water, then drain and set aside.
In a large skillet, heat the olive oil over medium heat. Add the minced garlic and sauté for about 1 minute until fragrant, being careful not to burn it.
Stir in the diced tomatoes (with juices), and cook for about 3-4 minutes, allowing the mixture to simmer and reduce slightly.
Pour in the heavy cream, stirring to combine. Bring the sauce to a gentle simmer.
Add the chopped spinach, basil, oregano, salt, and pepper to the sauce. Stir until the spinach wilts down (about 2-3 minutes).
Mix the cooked pasta into the sauce. If the sauce is too thick, gradually add some reserved pasta water until you reach the desired creaminess.
Stir in grated Parmesan cheese until melted and incorporated. If you're using nutritional yeast, add that alternatively for a cheesy flavor. Adjust seasoning if needed.
Serve immediately with an extra sprinkle of Parmesan or nutritional yeast and a pinch of red pepper flakes, if desired.
Notes
For a dairy-free option, use coconut cream and nutritional yeast.