In a large heavy skillet over medium-high heat, heat 2 Tbsp. tomato oil. Season shrimp with salt and black pepper and cook, stirring occasionally, until pink and opaque, about 3 minutes. Transfer shrimp to a plate or bowl.

Meanwhile, in a large pot of boiling salted water, cook pasta, stirring occasionally, until al dente according to package directions. Drain.

In the same skillet over medium heat, cook garlic, tomato paste, red pepper flakes, and remaining 2 Tbsp. tomato oil, stirring, until tomato paste deepens in color, about 1 minute. Add sun-dried tomatoes, broth, cream, and Italian seasoning. Bring to a simmer, scraping up any browned bits, and cook, stirring occasionally, until sauce slightly reduces, about 5 minutes. Add spinach and cook, stirring, until wilted, 1 to 2 minutes.

Add pasta, shrimp, and Parmesan. Cook, stirring, until pasta is coated and sauce is glossy; season with salt and black pepper. Remove skillet from heat, cover, and let it sit 2 to 3 minutes. Give pasta another stir to coat.

Divide pasta and shrimp among bowls. Top with basil and more Parmesan.