Place chicken breasts onto a cutting board. Cut a pocket, being careful not to cut all the way through and stopping before you get to the end of the chicken.
In a microwave-safe bowl, place broccoli and 2 tbsps water. Microwave for 3 minutes. Drain excess water. Place bell pepper, cheese, mayo, and the rest of the garlic powder into the bowl. Stir to combine.
Add olive oil to skillet and heat on the stovetop over medium-high heat. Carefully add each chicken breast. Cook 4-5 minutes on each side. Place the entire skillet of chicken in oven for 10-15 minutes. Remove and enjoy!