Season the chicken with salt and black pepper and heat 1 tablespoon olive oil in a large skillet over medium-high heat.
Sear the chicken for 3 to 4 minutes per side, until it reaches 165°F, then transfer it to a clean plate.
Add the remaining oil and cabbage to the skillet and cook for 4 minutes, stirring until the edges begin to wilt.
Whisk the broth, mustard, honey and vinegar, pour it over the cabbage and simmer for 3 minutes.
Return the chicken to the skillet and turn each cutlet through the glaze before serving over the cabbage.