Step 1Place the garlic in a food processor and pulse until minced. Add the remaining ingredients and pulse until mixture reaches a consistency of minced olives. Makes 1 3/4 cups.
Step 1Place the garlic in a food processor and pulse until minced. Add basil and pulse until finely chopped. Add parsley, salt, cayenne pepper, lemon juice and the egg, then pulse until combined.
Step 2Slowly pour the olive oil through the feeding tube while the processor is running, allowing the mixture to combine and create an emulsion. Makes 1 1/4 cups.
Step 1Slice the bread horizontally and lay the halves on a cutting board. Spread the tapenade on one half and the aioli on the other.
Step 2Thinly slice the hard-cooked eggs and make one layer of eggs on the bottom side of the bread; sprinkle lightly with salt. Layer the vegetables, salting to taste. End with arugula. Drizzle with oil and vinegar. Add the top half of the bread, press gently and cut into four sandwiches.