Roast the poblanos directly over a gas flame or under a broiler, turning occasionally, until they are charred all over. Transfer the poblanos to a bowl, cover with plastic wrap and let cool. Peel the poblanos. Using a small, sharp knife, make a small lengthwise slit in each one, near the stem end. Using kitchen scissors, carefully cut out the core and seeds, then remove the core and seeds without tearing the poblanos or enlarging the opening.

Preheat the oven to 425 degrees. In a small skillet, heat the vegetable oil. Add the diced onion, garlic and jalapeno and cook over moderate heat, stirring occasionally, until softened, about 5 minutes. Let the vegetable mixture cool, then stir in the Monterey Jack, Parmigiano-Reggiano and chopped cilantro. Press the cheese filling into 6 logs.

Lightly season the insides of the poblanos with salt. Carefully stuff the cheese filling into the poblanos and press the poblanos closed. Place the stuffed poblanos on a baking sheet and roast in the upper third of the oven for about 12 minutes, until the cheese is melted.

In a bowl, combine the grape tomatoes with the diced avocado, onion, cilantro, jalapeno and lime juice and season the salsa with salt and pepper.

Transfer the chiles rellenos to plates, spoon the salsa on top and serve.

The unbaked stuffed poblanos and the tomato-and-avocado salsa can be refrigerated separately overnight. Bring the chiles rellenos to room temperature before baking.