Begin by preparing your chicken: place each chicken breast between two sheets of plastic wrap and gently pound to an even thickness, about 1/2 inch. This helps the chicken cook evenly and makes rolling easier.
Season lightly with salt and pepper. Lay a slice of ham and a slice of Swiss cheese on each piece of chicken. Roll up tightly, securing with a toothpick if needed.
In a shallow dish, mix Dijon mustard, mayonnaise, and lemon juice. Brush the outside of each chicken roll with the mixture to add tang and moisture.
Dip each chicken roll into breadcrumbs, pressing lightly so they stick. For extra crunch and a richer crust, you can mix breadcrumbs with a little grated Parmesan.
Heat a large skillet over medium heat and melt the butter. Add the coated chicken rolls and cook until golden brown on all sides, about 6-8 minutes, turning occasionally. The internal temperature should reach 165°F (74°C).
While the chicken is browning, warm the tortillas in a dry pan or microwave for a few seconds to make them more pliable.
Transfer the cooked chicken rolls to a cutting board and let them rest for 2-3 minutes. Slice each roll into medallions if you prefer bite-sized portions, or keep them whole for a dramatic wrap.
Assemble the wraps: lay a tortilla flat, place a few slices of chicken on the center, then drizzle with a little extra of the Dijon-mayo sauce if desired. Roll tightly, tucking in the ends. If you like extra creaminess, spoon a small amount of warmed milk or cream over the filling before wrapping.
Optional finishing touch: if you want a warm, melty finish, return the wrapped tortillas to the pan for 1-2 minutes on each side to crisp the outside slightly and help the cheese melt through the center.