In a food processor fitted with the slicing disk, slice the Brussels sprouts.
In a large skillet, heat the oil over medium-high heat. Add the shallot and cook, stirring often, until beginning to soften, 2 to 3 minutes.
Add the Brussels sprouts, 1½ teaspoons salt, and ½ teaspoon pepper to the skillet and cook, tossing often, until the Brussels sprouts are tender, 4 to 6 minutes. Remove from heat and stir in the vinegar and poppy seeds.
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