Preheat oven to 350°F. 

Slice ¼ inch off the top of a head of garlic, exposing the tops of the cloves inside. Drizzle cut garlic with 1 tablespoon evoo, and wrap in foil. Place in oven and roast at 350°F for 40 minutes, or until the garlic is lightly browned, soft and very fragrant. 

Squeeze cloves of garlic into food processor or blender. Add olives and tomato paste and pulse until smooth.

Spoon garlic-olive mixture into a small bowl. Fold in mayonnaise and lemon juice, then season with salt and pepper. Cover and store dip in the refrigerator for up to 5 days. Serve with vegetable crudites, as a sandwich spread, a dip for Shabbat first course, or with Fritto Misto--a fried mix of vegetables, cheese, or fish.