Rinse pheasant; place in a large mixing bowl or small pot.
Stir 3 quarts water, 1 cup coarse salt and 1 cup honey in large pot until salt and honey dissolve. Add 1/2 bunch fresh thyme, peeled garlic cloves and black pepper.
Pour brine over pheasant. If the bird is not completely submerged, place in smaller bowl.
Refrigerate bowl with pheasant in brine at least 12 hours and up to 18 hours.
Position rack in bottom third of oven and preheat to 350°F.
Drain pheasant well; discard brine. Pat bird dry inside and out.
Squeeze juice from orange halves into main cavity. Add lemon rinds and remaining fresh thyme to main cavity.
Tuck wings under pheasant; tie legs together loosely to hold shape. Place pheasant on rack set in small roasting pan.
Rub pheasant all over with 1 tablespoons olive oil.
Roast pheasant 1/2 hour. Baste pheasant with 1/2 cup chicken broth. Continue to roast until pheasant is deep brown and thermometer inserted into thickest part of thigh registers 180°F, basting with 1/2 cup chicken broth every 15 minutes and covering loosely with foil if pheasant is browning too quickly, about 1 hour longer.
Transfer pheasant to platter. Tent pheasant loosely with foil and let stand 20 minutes.
Pour pan juices into large glass measuring cup. Spoon off fat; reserve juices for gravy.