1. Heat grill. With serrated knife, slice bread lengthwise in half, horizontally.
2. In food processor, pulse together butter, sun-dried tomatoes, pesto, garlic, salt and pepper until thoroughly combined and sun-dried tomatoes are chopped. Scrape into bowl; stir in 1 cup shredded cheese.
3. Grill bread, cut side down, until toasted, about 1-1/2 minutes. Spread butter mixture onto cut side of each half, dividing equally. Sprinkle with remaining cheese.
4. Grill bread, cut side up, over indirect heat, with grill covered, until topping is melted, 8 to 10 minutes. Let cool slightly. With serrated knife, cut into slices. Serve warm.