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Preheat the oven to 350°F. Line a baking sheet with parchment paper.
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In a serving bowl, combine the lemon juice, shallot, ¼ teaspoon salt, and olive oil and whisk to combine. Set the dressing aside.
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Put the cheese in a small bowl with a generous grinding of black pepper. Add the cayenne and mix well.
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Spoon 4 heaping mounds of cheese, 3 inches apart, onto the prepared baking sheet. Pat the mounds into 3-inch rounds (they will spread while cooking). Bake until golden brown and crisp at the edges, 6 to 8 minutes. Remove from the oven and transfer the parchment with the frico onto the counter. Let cool.
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Have ready a bowl of ice water. Cut the asparagus into 1/2-inch pieces. Bring a pot of well-salted water to a boil. Add the asparagus and boil until just cooked through and still bright green, about 4 minutes. Drain, pour the asparagus into the ice water to stop the cooking, and drain again.
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Add the asparagus, white beans, and parsley to the dressing. Toss, season with salt to taste, and serve with the frico alongside or crumbled on top.