Heat the olive oil and butter in a medium sauté pan. Add the chicken breasts and brown for 5 minutes on one side, flip and then brown for another 4 minutes or until an internal meat thermometer reads at least 135°F (63°C). Cover while cooking if desired. Remove the chicken breast to a separate plate after they are browned.

To pan grill the vegetables, melt the 1 tbsp. of the extra olive oil to the pan. Add the sliced onions and jalapeños and sauté until browned and golden, about 5 minutes over high heat.  Remove to a separate bowl. Add the remaining olive oil to the pan and add the cauliflower. Brown for 4-5 minutes then remove to a separate bowl.

For the sauce, set aside ¼ cup of the chicken broth in a small bowl. Whisk in the cornstarch and set aside. Add the remaining chicken broth to the cooking pan, scraping up any browned bits for the bottom of the pan. Stir in heavy cream, heating gently over medium low heat. Whisk the cornstarch mixture again then pour into the cooking pan. Stir until the sauce is slightly thickened. Add the shredded cheese, stirring until the sauce is smooth and the cheese is melted. Stir in the chile powder for color.

Return the chicken breasts and any accumulated juices to the pan. Add the cauliflower. Spoon the sauce over the chicken breasts and cauliflower and simmer for 1-2 minutes. Serve warm garnished with the onions and jalapeños.