Preheat the oven to 425 degrees. Use a sharp knife to carefully cut a slit, like a pocket, into each chicken breast. Do not cut through the chicken breast completely. You are creating a pocket for the stuffing.
Add the chopped broccoli to a small bowl with the water. Cook in the microwave for 1-2 minutes to soften the broccoli. Then in a medium bowl, mix together the broccoli, shredded cheddar cheese, cream cheese, Dijon mustard, garlic, salt, and pepper.
Heat the olive oil over medium-high heat in a heavy skillet. Sear the chicken breasts for 2-3 minutes on each side until browned. Cover the skillet with foil and bake for 15-17 minutes or until chicken is cooked through to 165 degrees. Let rest for 5 minutes before serving.