1Melt 1 tablespoon of the butter in a medium skillet or nonstick frying pan over medium heat. Add the shallot, garlic, dried thyme, and a pinch of salt and sauté, stirring frequently, until the shallot has softened, about 3 minutes.
2Add the mushrooms to the skillet, turn the heat to medium-high, and sauté, stirring frequently, until the mushrooms have softened and browned, about 5 minutes.
3Add the spinach and cook until it wilts, about 3 minutes. Remove the pan from the heat and set aside.
4Turn the broiler on and arrange a rack about 6 inches from the heating element. Smear a small baking dish with the remaining 1/2 tablespoon of butter and set aside.
5Heat a nonstick crêpe or frying pan over medium heat and add enough crêpe batter to make a thin crêpe (see recipe link in the note above). Remove the cooked crêpe to a plate and repeat with the remaining batter. You should end up with 3 crêpes.
6Lay the crêpes out on a work surface. Distribute the mushroom-spinach filling between the three crêpes, arranging it in a line along the diameter of each one. Sprinkle the Parmesan on the filling.
7Carefully roll up the crêpes to form cylinders. Place the rolled crêpes in the buttered baking dish and sprinkle with the remaining 2 tablespoons of Parmesan.
8Place the crêpes under the broiler to brown, about 2 minutes. Transfer the crêpes to a warmed plate and serve.