1. Cut the bacon into cubes and brown it in a casserole dish with oil. Transfer it to a plate.
2. In the same casserole dish, brown the peeled and chopped onion. Remove it.
3. Then sauté the pieces of meat. Once they are well browned, sprinkle them with 1 tablespoon of flour. Mix.
4. Pour in the white wine, then add the bacon and onion back in.
5. Add the peeled and chopped carrot, salt, pepper, and thyme. Stir everything together and cover with hot water. Put the lid on and let it cook over low heat for 1 hour and 30 minutes.
6. Twenty minutes before the end of cooking, add the washed and peeled button mushrooms.
7. Prepare the white sauce by melting the butter, adding the remaining flour, and stirring vigorously. Pour in a ladleful of the blanquette cooking juice. Mix and let it cook until the sauce thickens.
8. Pour the white sauce into the casserole dish.
9. Just before serving and off the heat, thicken the sauce with an egg yolk and heavy cream. Serve hot with rice.