Preheat oven to 350 degrees F. Rinse chicken and pat dry. Place between two pieces of parchment and use a meat mallet or the blunt end of a rolling pin to pound breasts to approximately 3/4" thickness (it's most important that they're even). Sprinkle with salt and pepper, then allow chicken to sit at room temperature.
In a mixing bowl, combine panko, onion powder, garlic powder, 1/4 teaspoon salt and a pinch of black pepper. Spread over a baking sheet in an even layer. Bake for 8 minutes, until light golden in color. Set aside to cool.
In a small bowl, whisk together mayo, mustard, oil and honey until creamy.
Use a sharp knife and slice breasts in half, forming 4 pieces, then carefully slice into each almost all the way, forming 2 connect halves. Place 2 slices Swiss cheese, then 2-3 slices ham on one half of each piece. Close with the other half.
Evenly cover chicken with honey mustard mixture, then press a generous amount of panko on top.
Bake for 28 minutes, or until no pink remains in the the thickest piece of chicken (just cut into it at 28 minutes, then add for a few more if you see pink).
Optional: broil for a few minutes, watching VERY closely, until a darker golden brown on top. Serve immediately. Reheat at 350 until warmed through. Leftovers will keep in the fridge up to 3 days. Do not freeze.