To prepare the curry paste, preheat oven to 375°F.
Wrap garlic and shallot in foil. Wrap ginger and lemongrass in foil. Bake at 375°F for 1 hour or until very tender and fragrant. Cool.
Squeeze pulp from garlic cloves into a food processor; discard skins. Add shallot, ginger, lemongrass, and next 6 ingredients (through chiles) to food processor; process until combined. Reserve 5 tablespoons curry paste for Curry-Poached Cod with Snap Pea Slaw and Thai Sweet Potato Noodle Bowls. Reserve 1/3 cup curry paste for another use.
To prepare chicken, combine remaining 6 tablespoons curry paste, milk, and 1 1/2 tablespoons oil in a large ziplock plastic bag. Add chicken; seal. Refrigerate 8 hours or overnight.
Preheat grill to medium (350°F to 400°F). Coat grill grate with cooking spray. Remove chicken from marinade; discard marinade. Sprinkle chicken evenly with salt and pepper. Arrange chicken on grill; cook 5 minutes on each side or until done. Place chicken on a platter; top with cilantro leaves and peanuts. Serve with lime wedges.