1. Slice eggs in half lengthwise; carefully remove yolks, keeping egg white halves intact. Process yolks, garlic, olives, and lemon rind in a food processor until combined, stopping to scrape down sides. With food processor running, gradually pour olive oil through food chute in a slow, steady stream, processing until mixture thickens. Stir in salt, pepper, and hot sauce to taste.
2. Spoon yolk mixture evenly into egg white halves. Garnish, if desired.