Start by heating the olive oil in a large skillet over medium-high heat until it shimmers and begins to gently ripple. Add the shrimp in a single layer, cooking them for about 2-3 minutes until they turn pink and are just opaque, then remove and set aside.
In the same skillet, add the minced garlic and cook for about 30 seconds until fragrant—listen for a gentle sizzle and smell the nutty aroma. Sprinkle in the chili flakes and stir for 15 seconds, allowing the heat to release their smoky aroma.
Pour in the canned crushed tomatoes, stirring well to scrape up any browned bits from the bottom of the skillet. Bring the sauce to a gentle simmer and cook for about 5 minutes until it thickens slightly and develops a rich aroma.
Return the cooked shrimp to the skillet, tossing gently to coat them evenly in the fiery tomato sauce. Cook everything together for another 2 minutes until the shrimp are heated through and the flavors meld.
Season the sauce with salt and freshly ground black pepper to taste. Tear fresh basil leaves and stir them into the sauce just before serving, releasing their bright aroma.
Serve immediately while hot, garnished with additional basil if desired. The sauce should be vibrant and thick, clinging to the tender shrimp, ready to enjoy with your favorite pasta or on its own.