In a blender, combine 1/4 cup olive oil, egg, lemon juice, garlic, salt, and red pepper. Blend until combined. Remove center of cover (or entire cover) and, at low speed, slowly pour remaining 3/4 cup olive oil into mixture in a steady stream; continue blending until thick. (Makes about 1 cup of aioli.)
In a small bowl, combine 1/2 cup aioli and olives.
Prepare the grill. Sprinkle beef with fleur de sel, and place on grill. Cook beef over medium heat, 6 minutes per side for medium-rare, or until desired doneness. Let cool 5 minutes.
Scatter arugula on a large platter. Slice beef, and lay slices over arugula. Serve with olive aioli.
Recommended ingredients: Davidson's pasteurized eggs are available online at safeeggs.com. Fleur de sel is available online at chefshop.com or at specialty food markets.