Make the ginger-chile butter: In a small bowl, using a spoon, mash together 2 tablespoons butter, shallot, ginger, jalapeno, lime juice, coriander, 1 teaspoon salt, and 1/4 teaspoon pepper. Set aside.
Preheat oven to 425 degrees. Using fingers, gently loosen skin from chicken breasts. With a small spoon, insert butter mixture evenly between skin and meat; pat skin back down. Tie chicken legs together with cotton kitchen twine; tuck wing tips underneath. Rub chicken with remaining 1/2 teaspoon butter; season generously with salt and pepper. On a rimmed baking sheet, arrange onions in a single layer; place chicken on top.
Roast until chicken is well browned and an instant-read thermometer inserted in a thigh (without touching bone) reads 175 degrees, 50 to 60 minutes. Transfer chicken to a cutting board and tent with oil; let rest 10 minutes (the temperature will rise by about 5 degrees).
On baking sheet, stir onions together with pan juices. Carve chicken; serve with onions and, if desired, lime wedges.