Use three plates or shallow bowls to set up your dredging station. In the first bowl, place the flour. In the second, place the two eggs and scramble them with a fork. In the third bowl, mix the breadcrumbs and parsley together.
Preheat oven to 350F.
Take one piece of chicken and place it in a quart sized bag (or between two pieces of plastic wrap, although the bag is easier). Using a meat pounder or something heavy like a rolling pin, pound the chicken until it is an even thickness of approximately 1/4".
Remove the chicken from the bag, set aside, and repeat with the remaining three pieces of chicken.
Place one piece of chicken on your work surface. Spread approximately 1 Tbsp of the apricot jam across the chicken but not all the way to the edge. Use less or more if desired, but too much will just squeeze out later.
On top of the jam, place one large or two small slices of ham.
On top of the ham, lay out some monterey jack or swiss cheese.
Slice some dried apricots in half lengthwise (to make them thinner and easier to roll). Place 3 or 4 across the chicken.
Starting at the pointed end, tightly roll up the chicken. If you press too hard everything will squeeze out. When you get to the end, secure everything in place using a few toothpicks.
Place the chicken in the flour dish and turn to coat. Shake off any excess flour.
Transfer the chicken to the egg bath, turning to coat. Let any excess egg drip off.
Transfer the chicken to the breadcrumb mixture, again turning to coat. Shake off any excess.
Place the chicken in a large baking dish. Repeat with the remaining chicken.
When all of the chicken has been rolled and dredged, place the chicken in the oven and bake until cooked all the way through, approximately 30-40 minutes. The exact thickness and size of the chicken will alter the cooking time. Use a thermometer to ensure that the chicken has cooked in the middle.
While the chicken is cooking, prepare any other sides such as rice and vegetables.
Sauce
While the chicken is cooking, make your sauce. Start by melting the butter in a small saucepan over medium heat.
When melted, whisk in the flour. Cook until the mixture has turned a light brown color.
Add the wine, chopped apricots, stock, and ground red pepper. Whisk to combine. Continue cooking over medium heat until the sauce is your desired thickness, approximately 7-10 minutes.
Season to taste with salt and pepper.
Serve everything warm with the apricot sauce. Remind your guests or family members that there are toothpicks in the chicken. I try to use the same number in every piece so that everyone knows exactly how many toothpicks they are looking for.