Poached Eggs with Mushrooms

1 stick (8 tablespoons) butter, divided
2 small shallots shallots
2 cloves garlic, chopped
2 1/2 pounds mixed mushrooms, trimmed (such as cremini, hon shimeji, white beech, trumpet, or velvet pioppini)
Salt and pepper to taste
1/2 cup white wine
1/4 cup Cognac
1 pint brown chicken base (such as Fond Brun de volaille; available at Whole Foods or 1 tablespoon chicken bouillon paste stirred into 2 cups chicken stock)
1 tablespoon white vinegar 
4 eggs
2 tablespoons chopped parsley
1 baguette, sliced and toasted

Sauté the mushrooms: in a large skillet set over medium heat, heat 4 tablespoons butter until it melts. Add the chopped shallots and garlic sauté until just transluscent, about 2 minutes. Increase the heat to high and add the prepped mushrooms and season with salt and pepper to taste. Cook until the mushroom soften and their juices evaporate, about 4 to 5 minutes.

Add the white wine and Cognac and cook until reduced by half, about 4 minutes. Add the chicken base and stir to combine. Cover and simmer for 20 minutes at low heat. Check the seasoning and add salt and pepper as needed. Finish with the remaining 4 tablespoons butter and set aside until ready to serve.

Poach the eggs: bring 2 quarts water to a boil in a deep saucepan. Add the white vinegar and slowly add the eggs. Poach the eggs for 4 minutes.

To serve, place the mushroom ragoût at the bottom of 4 serving dishes. Top with the poached eggs and add chopped parsley. Serve immediately with warm toasted slices of baguette.