Place a large skillet over medium-high heat with 2 tablespoons EVOO, about 2 turns of the pan.
While the pan is heating up, in a medium mixing bowl, combine the ground turkey with some salt and pepper and divide the meat into four portions. Shape each portion into a burger. Saut each burger in the hot skillet until golden brown and cooked through, about 6-7 minutes per side.
While the burgers are cooking, in a small bowl, stir together the garlic, shallot, Dijon, capers, thyme, and chicken stock. During the last two minutes of cooking, add the mixture to the pan and let it reduce, turning the burger once the mixture has thickened to coat.
Serve each burger on half of a toasted bun, pouring any remaining pan juices on top. Serve with your favorite salad or oven-roasted potatoes alongside.