In a large skillet, melt 1 tablespoon of butter over medium heat. Add the sliced onions and a pinch of salt.

Cook the onions, stirring occasionally, for about 10-12 minutes until they are soft and golden brown.

Stir in the balsamic vinegar and cook for another 2 minutes until the liquid has evaporated and the onions are glazed. Remove from pan and set aside.

While the onions cook, divide the ground beef into 4 equal portions and shape them into patties about 1/2 inch thick. Season lightly with salt and pepper.

In a shallow dish, mix the breadcrumbs with the chopped fresh thyme, salt, and pepper. Place the beaten egg in a separate shallow dish.

Dip each beef patty into the egg, allowing excess to drip off, then press firmly into the breadcrumb mixture to coat both sides.

Wipe out the skillet used for the onions and heat the remaining 2 tablespoons of butter and vegetable oil over medium-high heat.

Fry the breaded patties for 4-5 minutes per side until the coating is crispy and golden brown and the meat is cooked through.

Serve the hot karbonader immediately, topped generously with the warm balsamic glazed onions.