Step 1

For the crepe batter: Blend the milk, butter, sugar, salt, eggs and 1/4 cup water in a high-powered blender until fully incorporated, 2 to 3 minutes. Add the flour and blend again for an additional minute. Let the batter rest for 20 minutes before cooking.

Step 2

For the mushroom filling: Meanwhile, place a large cast-iron pan over medium-high heat and coat the bottom with neutral oil. Once the pan is hot, add the mushrooms so that they lay in a single layer. Leave the mushrooms undisturbed until fully browned on one side, 5 to 7 minutes. Flip the mushrooms over to their uncooked sides. Add the shallots and shake the pan to distribute. Turn the heat down to medium and stir until the shallots have softened slightly, 2 to 3 minutes. Add the garlic and thyme sprigs to the pan, stirring to combine, then season with salt and pepper. Deglaze with the white wine, shaking the pan to remove any browned bits, until it has almost evaporated. Add the heavy cream and stir. Cook until the cream reduces, the mushrooms are coated and glossy and a rich sauce remains, about 5 minutes. Season with salt and pepper. Reserve the mushroom filling until the crepes are ready to be filled.

Step 3

For the crepe cooking method: Place a large nonstick or crepe pan over medium heat. Using care, pour enough batter to thinly coat the bottom of the pan, about 1/4 cup, swirling as needed to cover any areas. Cook lightly on each side until very lightly golden brown, 30 seconds to 1 minute, before flipping the crepe to cook on the remaining side. Remove the crepe and hold until ready to be filled. Repeat with the remaining crepe batter.

Step 4

Fill the crepes with the mushroom filling and fold into squares or rectangles. Serve immediately.