Preheat the oven to 150°C.
Scatter the unpeeled garlic cloves, half the rosemary, and half the orange wedges into a roasting tin.
Stuff the chicken cavity with remaining orange and rosemary, and slide butter slices under the breast skin.
Place the chicken breast-side up on the garlic in the roasting tin.
Pour half a bottle of Cava over the chicken and cover the tin with foil.
Roast in the oven for 90 minutes.
Remove foil, turn the chicken upside down, and baste with tin juices.
Cook for 20 minutes to brown the underside, then turn the chicken back over.
Baste again, increase oven to 180°C, and cook until browned and juices run clear.
Remove chicken from the tin and let it rest in a warm place.
Discard large solids from the tin juices, reserving any soft garlic pulp for a clean pan.
Combine roasting juices, garlic pulp, remaining Cava, and white wine in the pan.
Simmer with tarragon until reduced by half, then whisk in a knob of butter.
Carve the chicken and serve with the reduced tarragon and garlic gravy.