Bring a large pot of salted water to a boil over medium-high heat. 
Add oil to a large, wide pot and bring to a simmer over medium heat. Add in the crushed red pepper flakes, tomatoes, salt, and pepper, and cook until the tomatoes begin to burst and give off their juices, about 9 to 10 minutes.

Use a wooden spoon to gently press the tomatoes if they're not bursting on their own. 

Add in the garlic and cook for 1 minute, or until fragrant. Stir in the broth and bring to a boil, then reduce the heat to a simmer and cook for 5 minutes. Finally, stir in the spinach and cook until slightly wilted. 

In the meantime, add the pasta into the boiling water and cook for 9 to 10 minutes, or until al dente.
Drain the pasta, reserving a 1/2 cup of the pasta water.
Toss the pasta immediately into the pot with the sauce and stir well to combine.

Add in some of the reserved cooking water, if needed. Taste and add additional salt and pepper, if needed.