Heat a large skillet over medium heat and add the olive oil. When it shimmers and begins to smell fragrant, add the minced garlic. Sauté for about 30 seconds until fragrant and slightly golden.
Sprinkle in the red chili flakes and stir for 15 seconds until they crackle and release their fiery aroma.
Pour in the crushed tomatoes, stirring well to combine with the garlic and chili flakes. Bring the sauce to a gentle simmer, then reduce the heat and let it cook for about 10 minutes, stirring occasionally, until it thickens slightly and turns a vibrant red.
While the sauce simmers, season the shrimp with salt and pepper. Heat a separate pan or adjust the same skillet, then add a little more oil if needed. Sear the shrimp over medium-high heat for 2-3 minutes per side until they turn pink, opaque, and develop a slight char at the edges.
Gently add the cooked shrimp to the tomato sauce, tossing to coat evenly. Let everything cook together for another 2 minutes, allowing the flavors to meld and the shrimp to soak up that fiery, garlicky goodness.
Finish by stirring in torn fresh basil leaves, releasing their bright aroma into the sauce. Turn off the heat and let it rest for a minute before serving.
Serve the Shrimp Arrabbiata immediately over cooked pasta or with crusty bread, garnished with extra basil if desired. Enjoy the fiery, fragrant, and perfectly tender shrimp in this bold, comforting dish.