Use a sharp knife to cut wonton wrappers diagonally in half to make triangles. Lightly coat a baking sheet with cooking oil/spray. Arrange one-third of the triangles in a single layer on the baking sheet. If desired, for ruffled chips, line baking sheet with foil. Shape foil to make ridges. Lightly coat foil with cooking spray. Place wonton triangles on foil, drapping over foil ridges.
In a small bowl stir together the olive oil, garlic and basil. Lightly brush the wonton triangles with one-third of the oil mixture; sprinkle with one-third of the cheese.
Bake in a 350 degree oven about 8 minutes or until golden. Cool completely on a wire rack. Repeat with the remaining wonton triangles, oil mixture and cheese.