Asparagus and Caramelized Onion Flatbread

Heat the oven to 400°F. Trim, peel, and thinly slice the onions. Put 2 tablespoons oil in a large skillet over medium heat. Add the onions and a pinch of salt and cook, stirring occasionally and adjusting the heat so they don’t burn, until they’re caramelized, 20 to 30 minutes.

Grease 2 large rimmed baking sheets with 1 tablespoon oil each. Put the flours in a large bowl with the cornmeal, baking powder, and 1 teaspoon salt and mix together with your hands. Add 6 tablespoons oil and 1 cup warm water and mix until smooth and elastic; the dough should come together in a well-defined, fairly sticky, but easy-to-handle ball. If you’re having trouble handling it, wash the excess dough off your hands. If it’s too dry, add more water 1 tablespoon at a time, mixing well after each addition.

Divide the dough into 2 balls and press out each into a 1/4-inch-thick round on one of the baking sheets; coat your hands with a little oil if the dough is sticking to them. Cover the dough with foil and bake until it’s set but still a bit soft and light-colored on top, 10 to 15 minutes. Remove the foil and cook until the crust is browned and crunchy, another 5 to 10 minutes.

Rinse, dry, and halve the lemon; juice it into a food processor. Drain and rinse the beans; transfer to the food processor and sprinkle with salt and pepper. Pulse until they’re smooth, adding water 1 tablespoon at a time as needed; taste and adjust seasoning. Add the vinegar to the onions and scrape up any brown bits from the pan; remove from the heat.

Rinse and trim the asparagus. Use a peeler to make long ribbons, turning each stalk as you work until you can’t make any more; finely chop the remaining stalk. Spread the bean puree evenly over the crust. Scatter with the onions and top with the asparagus, 2 tablespoons oil, and a sprinkle of salt and pepper. Cut into wedges and serve.