Preheat oven to 350°F. Place a wire rack on a rimmed baking sheet and spray lightly with cooking spray. Pound each chicken breast between plastic wrap to an even 1/4-inch thickness.

Lay 2 slices of ham on each breast. Add a heaping 1/4 cup Gruyere down the center, leaving a 1/2-inch border. Roll tightly from the narrow end, folding ham over the cheese at the end. Secure with 2 to 3 toothpicks.

In a skillet over medium heat, melt butter with olive oil. Toast panko for 3 to 4 minutes, stirring constantly, until golden. Transfer to a shallow dish, cool completely, then mix in Parmesan and all spices.

Whisk Dijon mustard, honey, and olive oil together in a shallow dish. Brush each chicken roll with the Dijon wash on all sides, then press panko firmly into every surface. Place on the prepared rack.

Bake for 30 to 35 minutes until internal temperature reaches 160°F. If tops brown too quickly in the last 10 minutes, tent loosely with foil. Remove toothpicks and rest 5 minutes before slicing.

Whisk all Dijon cream sauce ingredients in a small saucepan. Bring to a boil, reduce heat, and simmer 5 to 7 minutes until thickened. Slice chicken rolls on the diagonal, drizzle with warm sauce, and garnish with fresh parsley.