Combine turkey, ½ cup yogurt, bread crumbs, 2 tablespoons Dijon, oil, thyme, Worcestershire, ½ teaspoon salt, ½ teaspoon pepper, and fennel seeds (mixture will be fairly wet). 

Divide meat into 4 equal portions, gently form each into a ball, then lightly flatten into 1-inch-thick patties. Press finger through center of patties (this helps them patties flat) and transfer to a plate; chill patties at least 15 minutes or up to 2 hours.

Meanwhile, combine ½ cup yogurt, 4 teaspoons Dijon, lemon juice, garlic, and honey for the sauce; season with salt and pepper.

For a gas grill:

Heat grill over high for 15 minutes; clean and oil grill grate. Transfer patties to grill and cook, covered, without pressing down, for 5–7 minutes, flipping halfway through cooking.

Reduce heat to medium and continue to cook, covered, until an instant-read thermometer, such as the Thermapen, inserted into the center of the burgers reaches 160°, 5–7 minutes more.

Transfer burgers to a plate, tent with foil, and let rest 5–10 minutes.

For a skillet or grill pan:  

Heat a cast-iron skillet or grill pan coated with nonstick spray over medium until nearly smoking.

Transfer burgers to grill pan and cook, without moving, until bottom sides are dark brown and crusted, 3–4 minutes. Flip burgers and cook until starting to brown, but not crusted, 3–4 minutes more.

Reduce heat to low, cover pan with lid slightly ajar to let steam out, and cook 8–10 minutes more, flipping as needed to prevent burning, until an instant-read thermometer, such as the Thermapen, inserted into the center of the burgers reaches 160°, 7–10 minutes more.

Transfer burgers to a plate and let rest 5–10 minutes.  

Turn grill to low (or use skillet/grill pan) and grill buns, cut side down, until toasted 1–2 minutes.

Serve burgers on toasted buns, with sauce, lettuce, and pickled onions.