Preheat the sous vide bath to 148°F (64°C).
Prepare the chicken: rinse briefly under cold water and pat dry. Place breast-side down on a cutting board and use kitchen shears to cut along both sides of the backbone to remove it; discard or reserve for stock.
Flatten the chicken by pressing down on the breast until it lies relatively flat to promote even cooking.
Season both sides with 1/2 teaspoon salt and 1/4 teaspoon black pepper. Rub 1/2 tablespoon diced garlic and 1/4 teaspoon dried oregano into the skin side.
Place the seasoned chicken in a large vacuum bag in a single flat layer and add 3 slices of orange to the bag. Vacuum seal the bag.
Cook the sealed chicken in the sous vide bath at 148°F for 6 hours.
When cooking is complete, remove the bag from the water and chill in an ice bath for 5–10 minutes; then refrigerate if not finishing immediately.
Preheat the oven broiler to high. Open the bag, transfer the chicken to a cutting board, discard the orange slices from the bag, and gently wipe away excess moisture; pat the chicken dry.
Place the chicken on a rack set over a rimmed baking sheet. Brush or spoon the 2 tablespoons melted butter over the top of the chicken.
Broil the chicken on high for about 3–8 minutes, watching closely, until the skin is golden brown and crisp.
Remove from the broiler and let the chicken rest 15–30 minutes tented loosely with foil (poke a small hole for steam to escape). Serve with remaining orange slices and a sprinkle of fresh parsley if desired.