Preheat your oven to 350 degrees Fahrenheit.

In a small mixing bowl combine the cream cheese, 2 tbsp butter, garlic, dill, basil, parsley, thyme, ¼ tsp salt, and ¼ tsp black pepper. Carefully fold in the crab meat so it gets mixed in but doesn’t create a crab paste.

Slice the 3 chicken breasts in half, widthwise, so you have two chunky halves. If you cut them in half lengthwise, they will to be too thin to stuff. Place a chicken breast half on a plastic cutting board and cover it with plastic wrap. Tenderize the chicken with a meat tenderizer until it reaches half of its original thickness. Turn the chicken over and flatten it with the tenderizer again until it is very flat, about ¼ of an inch thick. Set the first piece aside and repeat these steps with the remaining chicken breast halves. If you don’t have a meat tenderizer, a rolling pin or wine bottle also works.

Divide the crab mixture into 6 portions. Transfer a flattened piece of chicken back to your plastic cutting board. Set one portion of the crab mixture in the middle of the chicken breast and roll the chicken around the mixture. Repeat with the other 5 chicken breast halves.

Pour the flour onto a small plate and season it with the ½ tsp of salt and ½ tsp of black pepper. In a small bowl, whisk or fork beat the two eggs with a splash of water. Spread the bread crumbs onto a small plate. Dredge one of your chicken breasts in the flour, rolling it around carefully to fully cover it. Shake off the extra flour and then dip it in the egg mixture quickly just to cover it. Pull the breast out of the egg mixture letting any extra egg fall off, and place it into the bread crumbs. Roll the breast again carefully to cover it with the bread crumbs and then gently shake it to remove extra crumbs. Set the chicken aside and continue the process with the other 5 pieces.

Lightly grease a baking sheet or large cast iron skillet with oil, and begin searing your crab-stuffed chicken breasts. Cook them in the oven for about 35 minutes until the bread crumbs are nicely browned and the chicken is cooked through. If you have gone past the 35-minute mark and your bread crumbs are still pale, broil the chicken on the low setting just for a couple of minutes to get a nice golden finish.

While the chicken is cooking, bring the white wine to a boil in a heavy bottomed sauce pan. Reduce the heat and add in the heavy cream and 3 tbsp of butter. Simmer the mixture over low heat until about a third of the liquid has evaporated. Mix in the Parmigiano-Reggiano cheese and let the sauce sit over a low heat until you are ready to serve the chicken.