Preheat oven to 400°F.
Season chicken thighs with salt and pepper on both sides.
Melt 2 tablespoons butter in a large cast-iron skillet over medium-high heat. Add chicken thighs, skin-side down, and sear both sides until golden, about 3 minutes per side. Remove chicken from pan and set aside.
Melt remaining tablespoon of butter in the skillet. Add garlic cloves and stir frequently until golden brown.
Add the wine to the pan and scrape up any chicken bits with a wooden spoon or spatula. Stir in the brown sugar, honey and fresh thyme until combined, then add the seared chicken back to the pan.
Place the skillet into the preheated oven and roast until completely cooked through, reaching an internal temperature of 165°F, about 25-30 minutes.
Remove the chicken from the pan and add the flour, cream and lemon zest to the drippings. Allow the sauce to come to a boil and remove from heat. Stir in more white wine to the sauce if it appears too thick.
Serve chicken over garlic mashed potatoes smothered in a spoonful of pan sauce, and garnish with fresh parsley and lemon wedges.