In a saucepan, sauté the bacon over medium-low heat until browned and lightly crispy, about 5 to 8 minutes. Remove from pan and set aside on a paper towel.
In the same saucepan, sauté the onion and carrot over low heat in the bacon drippings until onions and carrots are lightly caramelized, about 10 minutes. Stir in 1 tablespoon butter and then add the mushrooms. Continue cooking, stirring frequently, until mushrooms have released their water and are cooked through. Add garlic and cook, stirring for a minute, making sure it doesn’t burn. Add flour and stir for 2 minutes. Pour in the wine. Season with salt, pepper, thyme, bay leaves, and parsley. Let simmer, stirring occasionally, until wine is reduced by one-third and sauce thickens, about 25 to 30 minutes.
Meanwhile, prepare croutons by brushing melted butter on each baguette slice. Toast bread in a toaster oven in one layer until lightly browned. Remove from oven, rub toasts with garlic, and sprinkle with salt.
Two options for poaching the eggs: Option A: Poach eggs in simmering water for three to five minutes. Option B: poach the eggs in the sauce, carefully adding them one by one, and cooking for three to five minutes. Note: With Option B, the eggs will turn a dark purple color, which may not look as appetizing as Option A.
Ladle the sauce onto plates and sprinkle bacon on top of the sauce. Arrange two or three croutons on top of the sauce and place two or three eggs on top of the croutons. Sprinkle with parsley and serve immediately with a simple tossed salad and a glass of Bourgogne Pinot Noir.
