Preheat oven to 350 degrees. Break apart the head of garlic into separate cloves. Toss the unpeeled cloves with the olive oil, and season with salt and pepper. Throw in rosemary or thyme. Place the cloves in a pan and roast until soft, 20 to 25 minutes, covered.
To eat: squeeze the garlic from its skin and serve by itself or with French bread.
In a small bowl whisk together mayonnaise, garlic and lemon juice. Mayonnaise may be made 3 days ahead and chilled, covered.
Mix first 4 ingredients in medium bowl. Season with salt and pepper. Whisk egg and 2 tablespoons water in small bowl. Stir 2 tablespoons egg mixture into crab mixture (mixture will be dry). Discard remaining egg mixture. Form crab mixture into 4( 1/2 to 3-inch ) round patties, using about 1/2 cupful for each.
Heat oil in heavy large skillet over medium-high heat. Add crab cakes and saute until golden brown, about 4 minutes per side. Transfer to plates.