Preheat oven to 375°. Cut top off garlic head to expose tops of cloves. Wrap head in foil; bake until soft when pressed, 40 to 45 minutes.
When cool enough to handle, squeeze cloves into a food processor. Add mayonnaise, red peppers, bred crumbs, lemon juice, thyme leaves, kosher salt, hot sauce, and lots of freshly ground black pepper. Whirl until smooth.