Preheat your oven to 350°F.
Layer two pieces of plastic wrap on top of each other. Fold them in half, open and place a chicken breast near the fold. Fold over the plastic wrap covering the meat then gently pound and flatten the breasts using a rolling pin, meat pounder or the bottom of a heavy pot. Season the chicken, then spread a thin layer of Dijon over each piece. Lay two slices of ham and two slices of cheddar on each breast. Roll them up tightly.
Sauté the onions with the oil, dried thyme, salt and pepper. Continue cooking until they are lightly browned and golden. Place the chicken rolls on top of the onions in the pan or transfer to another baking pan, cover with a tight-fitting lid or foil and bake for 20-25 minutes, until the rolls are cooked through. You may serve them whole with a scoop of the onions or slice each one into several ‘rounds’ and present them on a bed of the onions.
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