Gruyère-Style Mushroom Thyme Crêpes with Mozzarella

Steps

1. Make the batter first: blend or whisk the flour, whole milk, eggs, water, half of the melted butter and half of the salt until smooth. Rest it 30 minutes at room temperature while you make the filling.
2. Heat the olive oil in a large skillet over medium-high heat. Add the mushrooms in an even layer and cook without stirring for 4 minutes, then stir and cook until browned and their liquid is gone, about 6 minutes more.
3. Add the garlic, green onion, thyme, black pepper and the remaining half of the salt to the mushrooms; cook 1 minute. Stir in the balsamic, then scrape the mushroom filling into a bowl and wipe out the skillet.
4. Heat the skillet (or an 8-inch nonstick pan) over medium heat and brush it lightly with some of the remaining melted butter. Pour in about 1/4 cup batter, swirl to coat thinly, and cook until the edges lift, about 1 minute; flip and cook 30 seconds. Stack the crêpes and repeat, brushing the pan with the remaining butter as needed, to make 8 crêpes. The eggs in the batter are cooked through once both sides are set.
5. Return 2 crêpes to the pan over medium-low heat. Sprinkle one quarter of the mozzarella over each pair, then spoon on one quarter of the mushroom filling. Fold into quarters, sprinkle with one quarter of the Parmesan, cover and warm until the cheese melts, about 2 minutes. Repeat with the remaining crêpes, mozzarella, mushroom filling and Parmesan.
6. Serve 2 crêpes per plate, scattered with the parsley.