Slice cherry tomatoes in half.
Roll basil leaves and chiffonade—slice very thinly into ribbons.
Cook pasta according to directions for al dente.
Drain the pasta—do not rinse—and reserve 1 cup of pasta water.
In a saucepan over medium heat, add enough olive oil to cover the bottom of the pan. Add fresh minced garlic and saute until garlic is just starting to brown. Add tomatoes. Saute until the skin on tomatoes starts to wilt.
Add ¾ cup of asiago cheese and a ladle of the reserved pasta water. Toss in the pan. Consistency should be creamy, not sticky. Add more reserved pasta water as needed to reach desired consistency.
Add ¾ of the basil leaves and toss. Add salt and pepper to taste.
Serve and garnish with remaining basil leaves and a touch of the shredded asiago.