Brush both sides of the bread with olive oil. Grill the bread slices until they begin to turn golden, about 1 to 2 minutes. Remove from the panini grill and place 2 ounces of cheese on 1 slice of bread (the bottom half), top the cheese with 1/3 cup chocolate chips, and a sprinkle of basil. Top with another slice of bread. Continue with the remaining sandwiches. Return the sandwiches to the panini grill until the chocolate begins to melt, about another 2 minutes.
Cut the sandwiches into 2-inch wide rectangles or small triangles and transfer to a serving platter.