Slice a pocket into each chicken breast without cutting all the way through the meat.
Spread a portion of the garlic-and-herb goat cheese in the middle of the pocket and then place three asparagus stalks on top of the cheese (if needed, use a toothpick to secure the ingredients).
Sprinkle each stuffed chicken breast with salt and pepper.
Heat the olive oil and butter in a heavy-bottomed saucepan, then add the minced garlic.
Add the stuffed chicken breasts to the pan and cook for about six minutes on one side.
Flip the chicken breasts to sear the second side and add the chicken broth. Cover the pan and cook until the chicken is fully cooked.
Remove the toothpicks (if used), slice and serve with whole grain rice or pasta.