Bring a large pot of water to a boil. (For 12 eggs, use about 4 qt. water.) Using a slotted spoon or tongs, gently lower eggs, one at a time, into water. Return to a boil, cover, and reduce heat to medium-low. Cook for 12 minutes.

Meanwhile, in a medium skillet over medium-high heat, heat oil until shimmering. Cook corn, stirring frequently, until browned, about 5 minutes.

A few minutes before eggs are cooked, fill a large bowl with about 4 cups ice and about 6 cups water. Transfer eggs to ice bath. Let sit about 30 seconds.

Using the back of a spoon, tap each egg, making sure to tap all over shell. (Alternatively, you can tap and roll the eggs on a counter; keep in mind not to tap the eggs too hard!) Return cracked eggs to ice bath and let sit 5 minutes. Peel eggs under a thin stream of cool running water, or peel while still in ice water.

Slice eggs in half lengthwise. Scoop yolks into a food processor; reserve egg whites. Add mayonnaise, sour cream, lime zest, chili powder, chipotle chile, salt, and ½ cup corn to yolks. Blend until smooth.

Transfer filling to a medium bowl. Fold in ½ cup corn kernels.

Arrange reserved egg whites on a platter. Transfer yolk mixture to piping bag fitted with large star tip. Pipe filling into egg whites.

Top with cotija, cilantro, and remaining corn. Dust with hot Cheetos (if using). Refrigerate until ready to serve.