Cook garlic in medium saucepan of simmering water until very soft, about 20 minutes. Drain; cool. Peel garlic. In food processor, pulse a few times to chop coarsely. Add goat cheese and blend well. Toss in basil, oil, chives, cilantro, and rosemary and pulse quickly. Season with salt, pepper, and cayenne. Cover and refrigerate. Serve with homemade crostini or good flatbread crackers.
(Can be made 3 days ahead, the "curing" time enhances the flavor.)