Preheat oven to 400. Arrange oven racks so a large skillet and baking sheet can fit at the same time.
2
Melt 3 tablespoons butter in a saucepot over medium heat. When butter foams, whisk in 3 table in stock and spoons flour, cook 1 minute then whisk warm half and half. Let thicken and season with salt, pepper and nutmeg to taste. Stir in cheeses and keep warm over low heat.
3
Preheat a large, cast iron skillet over medium high heat.
4
Cut chicken away from bones, keeping the skin intact. Place chicken between wrap or parchment and pound to 1/2 inch thick. Season on both sides liberally with salt and pepper. Dredge very lightly in flour, shaking off all excess.
5
Arrange broccolini on a baking sheet and toss with 2 tablespoons or so olive oil, garlic, salt and pepper. Roast 15-18 minutes until crispy at edges of broccolini tops.
6
Add olive oil, 1 turn of the pan to skillet and melt remaining tablespoon butter into oil. When it foams, add chicken skin side down; press down on chicken as it cooks with spatula to make skin extra crispy. Cook 5-6 minutes then transfer to oven for 5 minutes more. Remove, turn the chicken and let stand a minute or two. Transfer to plates and douse with lemon juice.
7
Plate the chicken with roasted broccolini alongside. Ladle the mornay sauce over the top of broccolini and chicken. Garnish with crispy onions and serve.