Place chicken breast flat on a cutting board, using a sharp knife, about 1/3 of the way down the thick side, cut a deep pocket horizontally into the center of the meat about 3/4 of the way down, being careful not to cut through to the other side. Repeat with the remaining breasts. Wash hands well.
Season each pocket with salt and pepper.
Place a slice of ham in each pocket.
Cut the Fresh Goat Cheese Log in quarters. Wrap each cheese slice with ham. Place each wrapped quarter into each pocket that was made in the chicken breasts.
Wrap each stuffed chicken breast and place in refrigerator to chill for 30 minutes.
Set up a standard breading procedure using 3 shallow containers. Put flour in the first one, eggs and milk in the second, and Panko or bread crumbs in the third one.
Beat the eggs and water together.
Dredge each of the stuffed Chicken Breasts first in flour, then egg wash and then in the Panko or bread crumbs.
In a large, oven-proof skillet, heat the oil over medium-high heat. Add the chicken and sear until golden brown, 2 to 3 minutes on each side.
Place the pan in the oven and bake in the oven until the chicken is cooked through, 7 to 10 minutes.