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.