Preheat oven to 400°F. Line a rimmed sheet pan with parchment for easy cleanup.
Pound chicken between sheets of plastic to about 1/4 inch thick so it rolls easily.
Stir Dijon and mayonnaise with 1 tablespoon melted butter to make a spread.
Combine panko, Parmesan, garlic powder, onion powder, paprika, salt, pepper, and remaining melted butter in a bowl until crumbs are evenly moistened.
Lay chicken smooth side down. Spread a thin layer of the Dijon mixture over each piece.
Top each with ham and Swiss. Roll up tightly, tucking ends. Secure with toothpicks if needed, seam side down.
Brush the outside of each roll with remaining Dijon mixture to help crumbs stick.
Press rolls into the crumb mixture to coat all sides. Place on the prepared pan.
Bake 25–28 minutes, until golden and the thickest part reaches 165°F. Rest 5 minutes, then remove toothpicks and slice.