Set a 12-inch deep skillet with a lid over medium heat.

Put the chicken on a plate and season it with 3/4 teaspoon of the salt and 1/4 teaspoon of the pepper.

Add the chopped bacon to the dry skillet. Cook for 5 to 6 minutes, stirring now and then, until the bacon is browned and has given off its fat.

Transfer the bacon to a plate with a slotted spoon. Leave the fat in the skillet.

If the skillet looks dry, add the olive oil. Put the chicken into the skillet in a single layer.

Cook the chicken for about 4 minutes without moving it much, until the bottom side is browned in spots.

Turn the chicken pieces with tongs and cook for 2 to 3 minutes more, until the second side is lightly browned but the chicken is not fully cooked through. Transfer the chicken back to the plate.

Add the onion, carrots, and celery to the same skillet. Cook for 4 minutes, stirring often, until the onion starts to soften.

Add the cabbage, caraway seeds, the remaining 1/2 teaspoon salt, and the remaining 1/4 teaspoon pepper to the skillet. Cook for 4 to 5 minutes, stirring often, until the cabbage wilts down and looks glossy.

Add the rice to the skillet. Stir for 1 minute so the grains are coated in the fat and mixed through the vegetables.

Pour the chicken broth and apple cider vinegar into the skillet. Add the Dijon mustard and stir until the mustard dissolves into the liquid.

Use a wooden spoon to loosen any browned bits stuck to the bottom of the skillet. Those bits add flavor to the rice.