Preheat oven to 425-degrees. To spatchcock chicken, set on cutting board and using kitchen shears, cut along the left and right side of the backbone (follow from the outside of the tail) from tail to neck. Remove the backbone and discard (or save for soup!), turn the chicken over and press with heels of hands gently along chest cavity to flatten. Tuck wing tips under the breasts. Brush chicken all over with 1 tablespoon oil and place on a rimmed sheet tray or wide, shallow baking dish.
To prepare onions, cut off the top then slice in half from top to root. Peel off outer layer but leave root on. Cut each half into quarters from top to root. Each onion should yield 8 wedges, making 16 total wedges.
In a medium mixing bowl, combine onion wedges, garlic and oil. Toss to coat; distribute around the chicken. Generously season the chicken, onions and garlic with salt, pepper, tarragon and lemon zest.
Roast chicken in center of oven for 45-60 minutes, or until the thickest part of the breast reaches 165-degrees. When chicken has reached internal temperature, turn broiler to high and cook for 2-3 minutes to brown. Remove pan from oven, drizzle lemon juice over the top, then let rest for ten minutes.
Slice chicken on a clean cutting board and serve with the roasted garlic and onions.
For a visual tutorial on spatchcocking a chicken, see this video
This recipe works well with other herbs like thyme, rosemary and oregano.