Heat a large skillet over medium and add olive oil. Once shimmering, stir in the chopped garlic and cook until fragrant, about 30 seconds, until it just starts to turn golden.
Pour in the white wine and let it simmer gently for 2-3 minutes, scraping up any browned bits from the bottom of the pan. This adds a rich depth to the sauce.
Add the crushed San Marzano tomatoes to the skillet, along with a pinch of red pepper flakes. Stir everything together and bring to a gentle simmer.
Reduce the heat to low and let the sauce simmer uncovered for about 20-25 minutes, stirring occasionally, until it thickens slightly and turns a rich, vibrant red aroma fills the kitchen.
While the sauce simmers, prepare your shrimp by patting them dry thoroughly and seasoning lightly with salt and pepper. Set aside.
Gently place the shrimp in the simmering sauce in a single layer. Cook for 2-3 minutes per side, until they turn opaque, pink, and slightly curled. The sauce will crackle softly around them.
Once the shrimp are cooked through, turn off the heat. Stir in the chopped fresh basil for a bright, herbal aroma and color.
Taste the sauce and adjust salt if needed. For a finishing touch, drizzle with a little extra virgin olive oil and garnish with additional basil, if desired.
Serve immediately over cooked pasta or with crusty bread, enjoying the glossy, flavorful shrimp coated in the thick, homemade marinara.