Preheat the oven to 400˚F. In a medium skillet, melt the butter over medium heat. Add the onions and bay leaf; season with salt and finely ground pepper. Cook, stirring occasionally until the onions soften, about 15 minutes; reduce the heat if the onions begin to brown. Add ½ cup water. Increase heat a bit. Cook, stirring often, until the onions are golden, about 15 minutes. Add the apples, maple syrup, thyme, and nutmeg. Cook, stirring often, until the apples soften, 10 to 15 minutes. Stir in the Dijon. Remove the relish from the heat.
Heat a large cast-iron skillet over medium-high.
In a medium bowl, mix the turkey, Worcestershire, coarsely ground black pepper, white pepper, and granulated garlic; season with salt. Form into 4 patties (thinner in the centers for even cooking).
Add the oil to the skillet, one turn of the pan. Add the patties; cook, turning occasionally, until cooked through, 7 to 8 minutes. Top with cheese. Turn off heat. Tent the skillet with foil until the cheese melts, about 2 minutes.
Arrange some pickles on the bun bottoms. Top with the burgers, bacon, and apple-onion relish. Set the bun tops in place.