In a large pot or deep skillet, heat olive oil over medium heat.
Add minced garlic, red pepper flakes, dried oregano, and dried basil. Sauté for 1-2 minutes until fragrant.
Add the raw shrimp to the pot, season with salt and black pepper, and cook for 2-3 minutes until they start to turn pink. Remove shrimp from the pot and set aside.
Add the linguine pasta, diced tomatoes with juices, and chicken broth to the pot. Stir to combine.
Bring the mixture to a boil over high heat, then reduce heat to medium-low and simmer uncovered for 10-12 minutes, stirring occasionally, until the pasta is al dente and most of the liquid is absorbed.
Stir in the fresh baby spinach and cooked shrimp. Cook for another 2-3 minutes until the spinach wilts and shrimp are fully cooked.
Remove the pot from heat and stir in grated Parmesan cheese and chopped fresh parsley.
Serve immediately, garnished with extra Parmesan cheese if desired.