Blend the mint, basil, pine nuts, and garlic in a food processor until finely chopped. With the machine running, gradually add 1/4 cup of olive oil, processing until well blended. Transfer the pesto to a medium bowl. Stir in the Parmesan. Season, to taste, with salt and pepper.
Toss the shrimp with the extra-virgin olive oil in a large bowl to coat. Sprinkle with salt and pepper, and toss again.
Heat a heavy large skillet over high heat. Working in 2 batches, add the shrimp and saute until just cooked through, about 3 minutes. Toss the shrimp with enough pesto to coat.
Transfer the shrimp to a platter and serve.