Hard-boil the eggs: Place eggs in a single layer in a pot and cover with cold water by an inch. Bring to a gentle boil over medium-high heat. Once boiling, cover, remove from heat, and let sit for 10–12 minutes. Drain and transfer eggs to an ice bath to stop cooking. Peeling will be effortless after the chill.

Roast the poblano (if using fresh): Hold the poblano over a gas flame or broiler until skin is charred and blistered on all sides. Place in a bowl and cover with plastic wrap for 10 minutes to steam. Peel, seed, and finely chop.

Halve and scoop: Slice eggs lengthwise and gently remove yolks into a bowl. Arrange whites on a serving platter.

Make the filling: Mash yolks with mayonnaise, sour cream, lime juice, cumin, smoked paprika, salt, and pepper until smooth but still with small curds for texture. Fold in the chopped poblano, shallot, and cilantro. Taste and adjust seasoning.

Fill the eggs: Spoon or pipe the yolk mixture back into egg whites. Sprinkle with smoked paprika, cotija, and cilantro.

Serve and enjoy: Let the flavors mingle for 10 minutes at room temperature or chill and serve later.