Rachael's Apple-Dijon Turkey Cheeseburgers with Caramelized Onions

Heat a skillet over medium heat with 1 tablespoon olive oil, 1 turn of the pan. Add a pat of butter to oil and when it foams, add the onions, season with salt, and cook to caramel in color, 25-30 minutes, stirring occasionally. Add a bit of water if they begin to brown. Stir in light brown sugar and balsamic vinegar, let them dissolve and absorb, then remove from heat.  

Core one apple and thinly slice or use a mandoline. Heat a saute pan or skillet over medium heat with a couple pats of butter, and when butter foams, add the sliced apples and cook about 2 minutes on each side. Season apples with a little nutmeg, a few grates, and 1 tablespoon lemon juice, then remove from heat and reserve.

Peel and quarter, then core and grate remaining apple, and add about 1 teaspoon lemon juice.  

For burgers, in a bowl, combine turkey with Worcestershire, salt, black pepper, white pepper, grated apple, granulated onion, sage and Dijon mustard. Form 4 large thin patties, thinner at center for even cooking.  

Heat a large cast iron skillet or griddle over medium-high heat. Add oil, 1 turn of the pan, and cook patties 10 minutes, turning occasionally. Top with sliced apples and cheddar and/or blue cheeses, then lightly cover pan with foil or lid and melt cheese.

Build burgers: bun bottom, pickles, lettuce, cheeseburgers, apples, onions, bun top.