Remove steak from liquid and pat dry. In a heavy pan, melt 2 tablespoons butter in oil over high heat. Add meat and saute, turning constantly, until browned on all sides (about 5 minutes). Transfer to a plate and set aside.
Add cognac to pan and deglaze by igniting. Add 2 tablespoons butter and melt. Add flour and heat for 2 minutes, stirring constantly. Whisk in remaining Burgundy. Bring mixture to a boil and scrape pan. Add meat, thyme, pepper, garlic and bay leaf to pan and simmer over low heat for 30 minutes. Add carrots and onions and continue cooking for another 30 minutes.
In a saute pan, melt remaining 2 tablespoons butter over medium heat. Saute mushrooms until they release their liquid and are browned (about 5 to 7 minutes). Add peas to pan.
For topping: Clean, peel and cut potatoes into 1/2-inch slices. In a large pot, boil potatoes until tender, about 10 minutes. Mash potatoes. Beat in salt, melted butter, egg yolks and milk. Set aside.
Transfer beef mixture to a 1-1/2 quart baking dish and remove bay leaf. Spread potato topping over meat. Drizzle melted butter over the top and dust with nutmeg. Bake in a 350 degree oven for 15 to 20 minutes. If desired, brown potatoes by running under the broiler for 2 minutes.
Serves: 8 - 10