In a medium bowl, mix the ham and cheese. Gently slice a lengthwise pocket into each chicken breast. Stuff each breast with the ham and cheese mixture and secure with a skewer or a few toothpicks.
In a medium shallow bowl, add the flour and season with a pinch of salt and a few grinds of black pepper. In a second medium shallow bowl, add the mustard, paprika, eggs, a pinch of salt and a few grinds of pepper and whisk to combine. In the third medium shallow bowl, add the panko. Run each piece of chicken through these bowls in the order of setting them up: flour, egg then panko.
In a large straight-sided pan, add enough oil to just cover the bottom by about 1/4 inch. Heat on medium high and when the oil begins to swirl, add the chicken in batches, placing each piece in the oil away from you so there is less splatter. Add more oil between batches if needed. Cook until the chicken reaches an internal temperature of 160 degrees F, 10 to 15 minutes. Remove to a paper towel-lined plate and season with a pinch of salt and a tiny spritz of lemon.