Heat the olive oil in a 10- to 12-inch skillet over medium-high heat. Add the bratwurst and brown for 1–2 minutes per side. Transfer to a plate. The bratwurst will not be fully cooked at this point.
Reduce the heat to medium-low and melt the butter in the skillet. Add the onions and apples and sauté for approximately 5 minutes, or until the onions begin to soften.
Add the brown sugar, garlic and caraway seeds and sauté for 30 seconds, stirring constantly.
Add the drained sauerkraut, black pepper and chicken broth. Stir to combine.
Return the bratwurst to the skillet and nestle them into the sauerkraut mixture. Bring to a gentle simmer.
Cover, reduce the heat and simmer for approximately 20 minutes, turning the bratwurst occasionally, until they reach an internal temperature of 160°F (71°C).
Serve the bratwurst with the sauerkraut, apples and onions.
Notes
Note 1 - Lightly crush the caraway seeds before adding them to release more flavor. Use up to 3/4 teaspoon if you prefer a stronger caraway flavor.