Heat the olive oil in a wide, deep skillet or Dutch oven over medium heat. Add the garlic and cook for about 1 minute without browning it.
Add the white wine and simmer until reduced to about 1 tablespoon, about 5 minutes, scraping the bottom of the pan.
Stir in the chicken broth and lemon juice, scraping up any browned bits.
Add the frozen chicken thighs skin side up in a single snug layer. Bring to a bare simmer, cover, and cook over low heat for 50 to 60 minutes, adding water as needed to keep about a quarter inch of liquid in the pan.
Check the thickest part near the bone with an instant-read thermometer. It should reach at least 165°F (74°C); 175°F (80°C) gives meat that loosens from the bone.
Heat the broiler with a rack about 5 inches from the element. Transfer the thighs to a foil-lined broiler pan, skin side up, and blot the skin dry.
Skim the fat from the liquid in the skillet and simmer uncovered for 2 to 3 minutes to concentrate it.
Broil the chicken for about 5 minutes, until the skin is browned and crisp. Watch it closely.
Off the heat, stir the capers into the sauce, swirl in the cold butter until smooth, then stir in the parsley.
Spoon the sauce over the chicken and serve.