Finely grind basil, mint nuts, Parmesan and 1.5 tbs garlic in processor =2E Gradually add 1 c oil and process until pesto is well blended. Tran sfer to bowl. Season with salt and pepper. (Can be made 3 days ahead. Press plastic wrap onto surface, chill. Bring to room temperature before using.) Cook fettuccine in large pot of boiling salted water until tender but sti ll firm to bite, stirring occasionally.
Meanwhile, heat 2 tbs oil in large skillet over medium-high heat. Add sh rimp and 1.5 tbs garlic; saute until shrimp are cooked through, about 4= minutes. Remove from heat.
Drain pasta. Return to same pot. Add pesto and toss to coat. Transfer to large bowl. Arrange shrimp over pasta and serve.