Heat the 1/4 cup olive oil in a large skillet over medium heat. Add the 1 finely chopped yellow onion, 4 minced garlic cloves, and 1 teaspoon kosher salt. Cook until the onion softens, about 5 minutes.
Add the 1 (28-ounce) can crushed tomatoes and 1/2 cup white wine. Bring to a gentle simmer and cook until the onion is completely soft and the flavors have come together.
Add the 1 pound large shrimp and 1 tablespoon Calabrian chile paste (or red pepper flakes if using). Cook until the shrimp are just pink and opaque, about 2 minutes. Taste and season with more kosher salt if needed.
Sprinkle thinly sliced fresh basil over the top. Serve over pasta, polenta, or risotto, or with crusty bread.