Cook spaghetti according to package directions. Reserve about 1/2 cup of pasta water before draining.
While spaghetti is cooking, heat olive oil in a large skillet over medium heat.
Add minced garlic and red pepper flakes to the skillet and cook until fragrant, about 1 minute. Be careful not to burn the garlic.
Add the fresh spinach to the skillet in batches, stirring until it wilts. Pour in the vegetable broth.
Add the drained spaghetti to the skillet. Toss to combine with the spinach mixture.
Stir in the grated Parmesan cheese, salt, and black pepper. Add a little of the reserved pasta water if the sauce seems too dry, until it reaches your desired consistency.
Serve immediately.
Notes
This recipe is easily customizable. You can add other vegetables like cherry tomatoes or mushrooms, or a source of protein like cooked chicken or shrimp.