Preheat oven to 400 degrees Fahrenheit. In a small sauce pan over medium-low heat, melt butter, while stirring, with garlic, rosemary, salt, and balsamic vinegar. Stir until combined and completely melted. Remove from heat and let sit for 1-2 minutes to cool slightly, then stir in Asiago.

Slice the bread in a cross-hatch pattern with a serrated knife, making sure not to cut through the bottom of the bread. Insert spoonfuls of the mixture between the cuts. Pour remaining mixture, if any, over the top of the bread. Wrap and tent bread with foil and bake for ten minutes. Remove foil, return bread to oven, and bake for an additional 5 to 7 minutes. Serve immediately.