In a medium mixing bowl, whisk the salt into the beer until it dissolves. Then, whisk in yogurt, garlic, pepper, parsley, and sage until well combined.
Put raw turkey breasts in a gallon size sealable bag and pour brine over it. Seal bag and rest it in a flat bottom dish, like an 8” x 8” pan. Put pan in the refrigerator and marinate for 8-12 hours, flipping the bag over at least once during that time.
When reading to grill, take the bag out of the fridge. Remove turkey from brine and pat dry with paper towels. Let sit at room temperature while grill preheats. Discard brine.
Preheat gas grill by turning all burners on to a grilling temperature reaching between 450-500˚ F. Wrap a brick with clean aluminum foil and place it in the grill while preheating. (Using a brick is optional but is suggested if turkey breast doesn't lay flat on the grill.)
When grill is heated, turn off one burner, leaving at least one burner on. Spray or rub grill grates with oil on the OFF side only. Carefully lay turkey breasts on grill side with burners turned OFF, skin side down. Put on a heavy-duty oven mitt and place the brick on top of the turkey breasts (this step is optional).
Close the grill and let cook undisturbed for about 30 minutes. Check the temperature on your grill frequently and adjust level of the ON burner to keep grill temperature around 450˚ F (likely you will have to turn the ON burners up to a hotter temperature).
At 30 minutes, remove the brick while wearing the heavy-duty oven mitt and turn the turkey breast over. Take the temperature of the meat in 2 places. Remove turkey from the grill, likely when breast meat reaches 160˚ F. If temperature is still reading low, grill for 5-minute increments, skin-side up, checking the temperature each time.
Let turkey breasts rest on cutting board for 10-15 minutes untouched. Then, slice up meat or serve on the bone.