Heat up the water in a pot and add the salt and sugar. Stir until completely dissolved. Let the water cool down to at least room temperature, then add the whole grouse, ensuring they’re submerged in the water. Put the pot in the fridge and brine the grouse for 5-8 hours.
Drain and dry the birds with paper towels.
Boil rice for 45 minutes or until tender.
In a skillet over medium heat, melt the 2 tablespoons of butter and add the mushrooms and the onion. Cook for 8 minutes. Add the giblets and garlic and cook for another 5 minutes. Add the cooked wild rice. Add the thyme leaves, salt, and pepper to taste.
Stuff the rice mixture into the cavities of the birds. Rub the 1/4 cup of butter all over each bird. If the skin is still intact, be sure to rub some butter in under the skin, especially over the breasts. Season the exterior of the birds generously with salt and pepper.
Preheat oven to 475°F.
Put the birds on a sheet pan fitted with a rack, or in an oven-proof skillet and put in the oven for 15 minutes. Reduce the temperature to 350°F and continue cooking the grouse for an additional 15-20 minutes, basting with any accumulated butter from the bottom of the skillet.
Remove the grouse from the oven, cover with foil, and let rest for 10-15 minutes before serving. Enjoy!