Position an oven rack in the upper third of the oven and pre-heat to 400°F.
Fit a rimmed baking sheet with a baking rack.
Combine the artichoke hearts, pesto and 1/4 cup of the Parmesan in a food processor and pulse until finely chopped; 10 to 12 pulses; set aside.
Sprinkle the chicken cutlets with salt and pepper; arrange them, pounded-side up, on a work surface.
Divide the provolone evenly among the cutlets, leaving a 1/4-inch border around the edges; top evenly with the pesto and artichoke filling.
Starting at the short end of each cutlet, roll up to enclose the filling.
Secure with a skewer, or toothpicks, and season with more salt and pepper.
Put the flour in a shallow dish.
Put the eggs, in a second shallow dish, and beat until egg whites and yolks are well combined.
In a third shallow bowl, mix the breadcrumbs and remaining 1/4 cup Parmesan cheese.
Coat the chicken roll-ups first in the flour, then dip in the egg, letting any excess drip off.
Lastly, coat fully with the breadcrumb mixture and transfer to a plate.
In a large non-stick skillet, over medium-high heat, heat 2 tablespoons of the oil.
Put 3 of the roll-ups in the skillet, seam-side down, and cook, flipping as needed, until golden brown on all sides; about 5 minutes.
Transfer to the prepared baking sheet.
Wipe out the skillet and heat the remaining 2 tablespoons oil.
Cook the remaining roll-ups in the same method; transfer to the baking sheet.
Place in the oven and bake the roll-ups until cooked through; about 15 minutes.
Remove from the oven and remove the toothpicks before serving.
