Heat oven to 400°F. Cut crosswise slice from top of garlic head, removing tops of cloves (discard top). Place garlic head on 7-inch square sheet of foil. Drizzle 1 teaspoon oil over cut cloves; sprinkle with 1/4 teaspoon of the salt; wrap foil around garlic.
Roast garlic 35 to 40 minutes or until garlic is soft and golden brown. Cool 10 minutes or until cool enough to handle.
Squeeze roasted cloves from skins. Place each clove in garlic press; press garlic into small bowl. Add mayonnaise and remaining 1/4 teaspoon salt; mix thoroughly. Cover; refrigerate until ready to serve.
Place green beans in ungreased 15x10x1-inch pan. Drizzle 1 tablespoon oil over beans; toss lightly to coat. Sprinkle with 1/2 teaspoon of the salt.
Roast beans 12 to 15 minutes, stirring halfway through roasting time, until lightly browned. Transfer beans to serving platter. Sprinkle with remaining 1/2 teaspoon salt. Serve beans hot or cold with aioli and small tongs.