Heat olive oil in a large pot or deep skillet over medium heat.
Add minced garlic and red pepper flakes; sauté for 1 minute until fragrant.
Add raw shrimp to the pot and cook for 2-3 minutes until they start to turn pink. Remove shrimp and set aside.
Add diced tomatoes with juice, chicken broth, dried Italian seasoning, salt, and black pepper to the pot. Stir to combine.
Add linguine pasta to the pot, pressing it down gently to submerge in the liquid.
Bring the mixture to a boil, then reduce heat to medium-low and simmer uncovered, stirring occasionally, for 10-12 minutes or until pasta is al dente and liquid has reduced slightly.
Add fresh baby spinach to the pot and stir until wilted, about 1-2 minutes.
Return cooked shrimp to the pot and stir to combine. Cook for an additional 2 minutes until shrimp are fully cooked and heated through.
Remove from heat and stir in grated Parmesan cheese and chopped fresh parsley.
Adjust seasoning with additional salt and black pepper if needed.
Serve immediately, garnished with extra Parmesan and parsley if desired.