Melt the butter with the garlic in a large skillet over low heat. Allow to bubble slowly for about 10 minutes to infuse the garlic into the butter, then remove garlic and reserve.
Increase the heat to medium-high. When hot, brown the grouse until golden brown on both sides, about 3 minutes per side; then set aside.
Pour the sherry into the skillet and allow to simmer for 20 seconds. Stir in the chicken stock, tarragon, and peach jam; bring back to a simmer, then reduce heat to medium-low, cover, and simmer for 5 minutes.
Add the balsamic vinegar, and cook, covered for 2 minutes. Return the grouse to the pan, and simmer until fully cooked, 3 to 5 minutes.