Preheat oven to 400°F.
Lay chicken breasts between two layers of plastic wrap and pound with a meat tenderizer until uniform in thickness. Cut a pocket into each piece, leaving about ½” border along one edge. Put chicken in a mixing bowl and add olive oil and mustard. Mix and rub by hand to coat evenly. Lay chicken on your baking sheet and place two slices of cheese, folded in half, into each pocket. Sprinkle with ¼ teaspoon salt, pepper, and garlic powder.
Rough chop the Broccolini into 2” pieces. Toss Sweet Potato and chopped Broccolini with 2 tablespoons olive oil and remaining salt. Add vegetable mixture to the baking sheet, surrounding the chicken and bake on the middle rack for 25 minutes or until chicken reaches an internal temperature of 165°F.