Preheat oven to 375 degrees F. Heat butter in a saucepan over medium-low heat. Add sliced shallots and cook, stirring occasionally, until light brown, 8-10 minutes. Add flour and cook, stirring constantly, to make a blond roux, about 5 minutes. Slowly add milk and cream, whisking constantly to prevent lumps from forming. Raise the heat and bring the mixture to a boil. Reduce heat to low and simmer for 20 minutes, stirring occasionally. Remove from heat, taste, and season with salt and pepper. Set aside.
Heat 1 tablespoon of olive oil in a sauté pan over high heat until it shimmers. Add minced shallots and garlic and sauté for 30 seconds. Add half of the mushrooms and sauté until mushrooms are golden and the liquid they release starts to evaporate, about 3 minutes. Transfer the mushrooms to a bowl. Return the pan to the heat and add the remaining 1 tablespoon oil. Add remaining mushrooms and sauté until golden and the liquid starts to evaporate, about 3 minutes. Add wine and simmer until most of the liquid is absorbed, about 3 minutes. Transfer to the bowl with the other mushrooms. Stir to combine and let cool completely.
Add sour cream, parsley, and thyme to the cool mushroom mixture. Taste and season with salt and pepper. Working with one noodle at a time, spread about 1/3 cup of mushroom filling over the length of each noodle. Gently roll the noodles up, pushing in the filling at the sides as you go. Place each roll, seam side down, in a buttered 11 1/2 x 8-inch baking pan. Pour the shallot cream sauce evenly over the rolls and sprinkle with the Parmesan.
Bake the lasagnas until the filling is hot and the top is lightly browned, about 15 minutes. Serve at once.
Yield: 8 servings
Suggested Wine Pairings: Red Burgundy, Oregon Pinot Noir, Cotes du Rhone, Chinon
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