Preheat a grill, or preheat the oven to 400 degrees F.
In a bowl, mix together the meat, salt and pepper, and Roasted Garlic Paste.
Using your hands, form 4 individual burgers. Wrap in plastic wrap and refrigerate until ready to grill.
Cook the burgers over a hot fire or roast in the oven until desired internal temperature is reached, about 160 degrees for medium.
Split each loaf of levain bread and pull out some of the soft center to make a hole for the burger. Place the bread face down on the grill to toast.
Place the burger in the bread and serve with garnishes.
Combine the garlic and oil. Bring to a boil and then reduce heat to medium. Simmer until garlic is brown and soft. Smash garlic with the back of a spoon; keep some chunks.
Mix all ingredients together. Cover and refrigerate.
Heat a large skillet over high heat. Add the olive oil. When the oil is hot, arrange the mushrooms in a single layer. Don't stir! Let them sizzle until they have caramelized on the bottom, about 2 minutes. If you toss them too soon, they will release their liquid and begin to steam. When the bottoms are caramelized, toss the mushrooms and continue to cook over high heat for about 5 minutes.
Add the butter. Continue to cook, stirring occasionally, until the mushrooms are beautifully browned, about 2 to 3 minutes. Season with salt and pepper and add the shallots and garlic. Saute until the garlic is lightly browned, about 2 minutes. Add the thyme. Add the wine, reduce the heat slightly, and simmer until the mushrooms are glazed with the sauce. Add the parsley, transfer to a warmed bowl, and serve immediately.