Preheat the oven to 400 degrees F. Season the chicken with olive oil, salt and pepper. Place on a roasting pan and bake for 30 minutes. Reduce the heat to 350 degrees F. and continue to cook for 30 minutes. In a large saute pan, melt the butter. Add the ham and saute for 2 minutes. Add the onions. Saute for 1 minute. Add the garlic and mushrooms. Season with salt and pepper. Saute for 2 minutes. Add the peas and potatoes. Saute for 3 to 4 minutes. In a saucepan, combine the vinegar, wine, peppercorns, shallots, and tarragon. Bring the liquid to a boil and reduce to 1 tablespoon. Add 1 tablespoon of water. Add the egg yolks and whisk, over low heat, until frothy, about 3 to 4 minutes. In a steady stream, add the butter until the sauce thickens. Season with salt and pepper. Strain the sauce through a chinois and set aside. Remove the chicken from the oven and carve into 4 pieces (2 breast and 2 leg/thigh). To serve, spoon the potato mixture on the bottom of each plate. Lay the individual chicken portions on top of the potatoes. Spoon the Bernaise Sauce over the chicken and serve.
Recipe from Who's Your Mama, Are You Catholic, and Can You Make a Roux?, by Marcelle Bienvenu