Set a large pot of lightly salted water over high heat and bring to a boil. Add the pasta and cook, according to package directions, until al dente. Carefully scoop out ½ cup of the pasta water and reserve. Drain the pasta.
Heat the olive oil in a large sauté pan over medium-high heat. Add the shallots and cook, stirring frequently, until golden brown, about 5 minutes. Stir in the garlic and peas and cook, stirring occasionally, for 3 minutes. If you're using fresh peas, they should turn bright green.
Reduce heat to medium-low and add the cooked pasta along with the ½ cup of pasta water. Add the mizuna, crushed red pepper flakes, lemon zest, lemon juice, and feta cheese and stir to combine. Cook, stirring occasionally, until mizuna begins to wilt, 1-2 minutes.
Remove pan from heat. Season to taste with salt and pepper and drizzle with a little olive oil. Serve with sliced radishes and a sprinkle of feta cheese.
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