Add 3 tablespoons butter and two tablespoons olive oil to a large skillet set over medium heat. Add garlic and sauté until golden brown, approximately 1-2 minute.

Add chicken and season with salt and black pepper, as desired. Cook, stirring occasionally, until the chicken is nicely browned on all sides, approximately 7-8 minutes.

Transfer the chicken to a platter and set aside.

Add the lemon juice and chicken broth and deglaze the bottom of the skillet by gently scraping with a spatula. Simmer until the liquid is reduced by half, approximately 2-3 minutes.

Add remaining butter and oil to the hot skillet. Add the red cabbage and broccoli to the skillet and cook, stirring frequently, until the vegetables are just tender, approximately 2-3 minutes. Do not overcook.

Return the chicken to the skillet and stir to combine. Once chicken is heated through, remove from heat. Garnish with fresh parsley and serve immediately. Enjoy!