Preheat oven to 400 degrees F. Line a baking sheet with parchment paper.
Separate rolls into 18 pieces. Set aside.
Heat oil in a small skillet over medium heat; add garlic and saute until tender, about 1 to 2 minutes. Do not brown garlic. Remove from heat and add pepper, cool slightly, about 10 minutes. Add 1cup Asiago cheese and walnuts and mix to combine.
Roll each Sister Schubert's Soft Dinner Roll piece in cheese mixture and place on prepared pan.
Bake 7 to 10 minutes or until golden brown. In a small bowl combine the remaining 3 tablespoons cheese and basil together and sprinkle over bites. Serve warm.