Heat oven to 450°F. Line 2 rimmed baking sheets with parchment paper and arrange 2 pieces naan on each.
In medium bowl, toss Broccolini, kielbasa, and cherry peppers with oil and 1/4 teaspoon each kosher salt and pepper. Divide among naan pieces, then sprinkle with cheese.
Carefully crack 1 egg in center of each naan and bake, rotating positions of pans halfway through, until egg whites are set and yolks reach desired doneness, 8 to 12 minutes for slightly runny yolks. Serve sprinkled with flaky salt and more pepper if desired.
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