Bring a large pot of salted water to a boil. Add linguine and cook until al dente, about 8–10 minutes. Reserve 1/2 cup pasta water, then drain.

Pat shrimp dry, season with salt, pepper, and a pinch of red pepper flakes. Heat 1 tbsp olive oil in a large skillet over medium-high heat. Cook shrimp 2 minutes per side until pink. Transfer to a plate.

Reduce heat to medium, add remaining 1 tbsp oil to the skillet. Cook garlic and sun-dried tomatoes 30 seconds. Add chicken broth, scraping up any brown bits. Stir in heavy cream, Italian seasoning, and red pepper flakes; simmer 2 minutes. Whisk in Parmesan, then add spinach and cook until wilted, about 1 minute.

Return shrimp and drained pasta to skillet. Toss well, adding reserved pasta water a tablespoon at a time if needed. Serve immediately with extra Parmesan and black pepper.