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Preheat oven to 425 degrees. Move oven rack to the upper third of your oven.
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Use a peeler or zester to remove the zest of one lemon and set aside.
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With a sharp paring knife, carefully cut asparagus into long, thin strips (halved or quartered, depending on the thickness). Slice radishes paper-thin. Toss asparagus and radishes with 1 tablespoon freshly squeezed lemon juice and a generous pinch sea salt, and set aside.
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In a small bowl, whisk to combine 1 teaspoon lemon juice, 1 teaspoon olive oil, and a pinch sea salt. Toss dressing with mizuna and set aside.
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In a small bowl, stir remaining 2 tablespoons lemon juice into ricotta. Add sea salt and pepper to taste.
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Place flatbreads on 2 rimmed baking sheets (or just 1 if they'll fit), brush with olive oil, then layer mizuna and asparagus strips, and tuck radishes throughout. Scatter lemon zest over the top.
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Slide flatbreads into oven and bake just until vegetables have wilted slightly and breads are golden, 2 - 4 minutes.
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Dot ricotta mixture all over hot flatbreads. Drizzle remaining olive oil over the cheese and vegetables. When cool enough to handle, slice into triangles and serve.