Make the batter: in a large bowl, combine 1 cup chickpea flour, 1 ¼ cups water, 1 tablespoon olive oil, and ½ teaspoon salt. Whisk until completely smooth. Let stand at room temp for at least 30 minutes (or up to 24 hours in the fridge).
Meanwhile, start the filling: heat 2 tablespoons oil in a large skillet over medium-high heat. Add the mushrooms with a pinch of salt and pepper, and cook until they’re browned all over, stirring occasionally, about 8 minutes.
In a bowl or measuring cup, combine 1 cup broth, ½ cup milk, and 1 tablespoon miso, and whisk to dissolve the miso. Set aside.
Stir 1 minced garlic clove and 2 tablespoons all-purpose flour into the mushrooms and cook for 30 seconds. Then add the broth mixture. Bring to a simmer and cook until the sauce is thickened, 5 to 7 minutes.
Add the spinach a handful at a time, stirring until it wilts before each addition. Continue cooking until the spinach is completely wilted, 1 to 2 minutes more. Set the sauce aside and keep warm.
To cook the crepes, heat a small non-stick skillet over medium heat. Using a pastry brush or folded paper towel, lightly brush the skillet with oil. Pour in a scant ¼ cup of the batter and immediately swirl it around to coat the skillet – the batter should sizzle right away; if it doesn’t, the skillet isn’t hot enough. Cook for 1 to 2 minutes, until the crepe looks dry. Run a small spatula or butter knife around the crepe to loosen it, then slip the spatula underneath and flip the crepe. Cook for another minute or so.
Transfer to a plate and continue cooking the rest of the batter, brushing the skillet with more oil before each crepe. (You may keep the cooked crepes warm in a low-temp oven.)
Divide the filling among the crepes and serve immediately.
