Place each chicken breast between 2 sheets of plastic wrap on a cutting board and pound it with a meat tenderizer until it forms an even thin cutlet. The cutlet should flex easily for rolling while remaining intact with no torn spots.

Cover each cutlet with ham, then set the Swiss cheese over the ham rather than directly against the chicken. Leave a small border around the edges so the filling has room to stay enclosed.

Fold the ham edges around the cheese, roll the chicken up from the bottom, and secure the seam with toothpicks. The toothpicks should slide in with slight resistance and hold the roll firmly closed.

Add the Parmesan cheese, almond flour, pork rinds, smoked paprika, and ground pepper to a food processor and pulse until finely ground. The finished crumb blend should look uniform, with no large hard pieces remaining.

Transfer the crumb mixture to a shallow bowl and place the beaten eggs in a second bowl. Keeping the bowls separate makes it easier to coat each roll without clumps forming in the crumbs.

Dip each chicken roll in the beaten egg, then press it gently into the crumb mixture until coated on all sides. The coating should cling evenly, especially along the seam and both ends.

Heat a large skillet over medium heat with the butter and olive oil, brown the chicken on every side, then lower the heat to medium-low and cover until the chicken reaches at least 165°F. A steady sizzle and a deeply golden crust signal good browning before the covered finish cooks the center through.

While the chicken cooks, melt the butter in a saucepan over medium heat and simmer the chicken stock until it reduces by 1/3. The stock should smell more concentrated and leave a slightly thicker coating on the pan.

Whisk in the heavy cream, stone ground mustard, ground pepper, and a small pinch of salt. Keep the heat gentle so the cream warms with soft bubbles rather than a hard boil.

Simmer the sauce for 5 minutes, then gradually whisk in the grated Gruyere until the sauce thickens to your liking. The cheese should melt into a smooth, glossy sauce that coats the back of a spoon.

Remove the toothpicks from the cooked chicken, slice the rolls into pinwheels, and spoon the mustard cheese sauce over the top. Let the chicken sit briefly before slicing so the juices settle and the cheese center holds its shape.