Preheat a grill or grill pan to medium-high. Heat a small, heavy skillet over medium heat. Add the garlic and cook, tossing occasionally, until golden, about 7 minutes; discard the skins. Using a food processor, combine 1 clove garlic, the mint, almonds and 3 tablespoons olive oil; season with salt.
Using your fingers, spread the pesto under the skin of each chicken thigh. Season the thighs with salt and pepper. Grill, turning once, until the chicken is cooked through, about 35 minutes.
Meanwhile, in a small bowl, mash the remaining 2 cloves garlic with 1/8 teaspoon salt; stir in the remaining 1 tablespoon olive oil. Brush the garlic mixture onto the bread slices and grill garlic side down until toasted. Serve each thigh on a piece of garlic toast.