Bring a large pot of salted water to a boil and cook the pasta for 3 to 4 minutes until al dente, then drain and reserve 1/2 cup pasta water.
While the pasta cooks, heat olive oil in a large skillet over medium-high heat for 1 minute.
Add garlic and red pepper flakes to the skillet and cook for 30 seconds until fragrant.
Add cherry tomatoes and cook for 2 to 3 minutes until they start to soften and release juice.
Add the drained pasta, spinach, lemon zest, lemon juice, and 1/4 cup reserved pasta water, then toss for 1 to 2 minutes until the spinach wilts and the sauce coats the pasta.
Remove from heat, stir in Parmesan cheese, season with salt and black pepper, and serve immediately.