Boil water for the linguine, adding 1 tbsp of the olive oil and a pinch of salt to the water. Cook the linguine for 7-8 minutes (al dente), stirring every minute. While the pasta is cooking, heat a large skillet with remaining olive oil.
When th e oil is hot, add the shrimp to the skillet, sauteeing until the shrimp turns pink, about 3-4 minutes.
Add the garlic and the basil and cook an additional 2-3 minutes.
Add the butter, and toss in the pasta, making sure to coat the pasta with the sauce. Remove from heat.
Serve immediately and garnish with the Asiago cheese as desired!