In a large pot of salted boiling water, cook the fettuccine according to package instructions until al dente. Reserve 1 cup of pasta water, then drain and set aside.
In a large skillet over medium heat, add 2 tablespoons of olive oil. Once hot, add the shrimp and season with salt and pepper. Cook until pink and opaque, about 2-3 minutes per side. Remove the shrimp from the skillet and set aside.
In the same skillet, add the remaining tablespoon of olive oil and sauté the minced garlic for about 30 seconds until fragrant. Add the red pepper flakes and cherry tomatoes, cooking until the tomatoes are softened, approximately 4-5 minutes.
Reduce the heat to low, then stir in the heavy cream. Let it simmer for 2-3 minutes, then mix in the grated Parmesan cheese until smooth.
Add in the cooked pasta, shrimp, and fresh spinach to the skillet. Toss well to combine, allowing the spinach to wilt slightly. If the sauce is too thick, add a bit of reserved pasta water until the desired consistency is reached.
Taste and adjust the seasoning with additional salt and pepper if necessary. Remove from heat and garnish with fresh basil before serving.