Heat grill. With serrated knife, slice bread lengthwise in half, horizontally.
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.
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.
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.
