In a Dutch oven or other large, heavy-bottomed pot, cook the chopped bacon with the butter over medium-high heat until crisp. Remove the bacon and reserve it for serving. Leave the fat in the pot.
Sauté the maitake mushrooms for 3–5 minutes, until softened and starting to brown at the edges. Allow any excess moisture to cook off.
Add the onion, celery, carrot and garlic. Sauté until softened, about 3–5 minutes, stirring frequently.
Season with salt, pepper and paprika. Add the wine and simmer for 2–3 minutes to reduce. For an alcohol-free option, use an equal amount of additional broth instead.
Add the potatoes, bay leaf and chicken broth. Bring to a boil, then cover and reduce the heat to a gentle simmer. Cook for 7–10 minutes, or longer as needed, until the potatoes are fork-tender.
Whisk the flour with roughly 1/4 cup of cool water until smooth. Stir into the soup and simmer until thickened and the flour is cooked through.
Stir in the heavy cream and warm through gently, stirring often. Remove the bay leaf and season to taste with additional salt and pepper.
Serve topped with the reserved crispy bacon. If desired, garnish each bowl with additional larger pieces of separately sautéed maitake mushrooms.