In a large skillet over medium heat, melt butter. Add garlic and tomato paste and cook until fragrant, 1 minute. Add mushrooms and tomatoes and cook until mushrooms are tender and tomatoes are starting to burst, 5 minutes.
Add heavy cream and Parmesan and season with salt, pepper, and a pinch of red pepper flakes, then bring to a simmer. Add spinach and cook until sauce is thickened and spinach is wilted, 5 minutes.