Preheat your oven to 350°F.
Cut each raw chicken breast into approximately 4 small pieces (the number will depend on how big your chicken breast is to begin with.) Next prepare your ingredients for breading: Mix the flour, salt and pepper together in a large ziploc bag. Beat the eggs in a shallow bowl or dish. Finally, mix together the panko crumbs and parmesan cheese on a large plate.
Working with a few pieces of chicken at a time, add to the bag with the flour. Seal and shake the bag to coat the chicken completely. Remove the chicken from the bag, tapping off any excess flour. Dip the chicken in the eggs, letting any excess drip off, and then into the panko to coat completely. Repeat this process with the remaining pieces of chicken. (At this point you can freeze these nuggets for another day. Simply place them on a baking tray lined with parchment paper and once the tray is full, put it in the freezer for about 2 hours or until the chicken is frozen through. Transfer the frozen pieces to a freezer bag and store for up to 2 months in the freezer. Cook from frozen as explained below.)
After all the pieces are breaded, heat some olive oil over medium-high heat in a large skillet. Working in batches, add your chicken in one single layer, taking care not to overcrowd the pan. Cook, without disturbing until a nice golden crust forms. Flip the chicken and continue to cook until golden brown on the other side. Transfer the chicken to a baking tray lined with parchment paper. Repeat with the remaining chicken pieces. Transfer the chicken to the preheated oven and bake until completely cooked through, about 8 minutes longer.
While the chicken is cooking in the oven, make your mustard sauce. Whisk the eggs, sugar and mustard powder in a pot over low heat. Whisk in the vinegar and stir continuously so the eggs do not become lumpy. Once the sauce starts to thicken, stir in the butter. Pour into a serving bowl and cover the surface of the sauce with plastic wrap. Remove the wrap when ready to serve. You can also make this sauce a couple of days in advance and keep covered in the refrigerator until you are ready to use. I like to bring it up to room temperature before serving.
Once your chicken is cooked, remove it from the oven and skewer each piece before placing on a serving tray. Serve with the mustard sauce on the side.
The best part of these skewers is that you can make a big batch and freeze them. That way they also double as a great last minute dinner for the kids – no fancy sauce needed, just a bit of ketchup.