Preheat the oven to 400 F and line a baking sheet with parchment. Pound each chicken breast between two sheets of plastic wrap until about 1/4 inch thick, then season both sides with the salt and black pepper.
Layer 2 slices of deli ham and 2 slices of dairy free provolone on each chicken breast. Roll each one up tightly and secure with toothpicks, then chill for 15 minutes so the rolls hold their shape.
Set up three shallow bowls with the flour, the beaten eggs, and the panko mixed with the paprika.
Coat each chicken roll in flour, dip in the egg, then press firmly into the panko until fully coated. Place on the baking sheet and spray generously with olive oil spray.
Bake for 25-30 minutes until the coating is golden and the chicken reaches 165 F inside.
While the chicken bakes, melt the dairy free butter in a small saucepan over medium heat. Whisk in the flour and cook for 1 minute.
Slowly whisk in the almond milk and simmer for 2-3 minutes until thickened. Whisk in the dijon mustard, nutritional yeast and salt until smooth.
Rest the chicken for 5 minutes, remove the toothpicks, and serve sliced with the warm dijon sauce spooned over the top.