1. Preheat broiler.
2. Combine first 8 ingredients (through garlic); pulse until blended. Slowly add oil through food chute with food processor on; process until smooth. Set aside 1/4 cup sauce; reserve remaining sauce for another use.
3. Split sandwich rounds; cut out 32 (1 1/4-inch) circles using a sharp round cookie cutter. Arrange bread in a single layer on a baking sheet; top evenly with cheese. Broil 3 minutes or until cheese melts. Remove from oven. Top each with 1 slice chorizo, 1/4 teaspoon romesco, and 1 parsley leaf.