How to Make It
Preheat the broiler and position a rack 2 inches from the heat. Spread the poblanos on a baking sheet and broil, turning occasionally, until blistered and blackened, about 15 minutes. Transfer to a large bowl, cover with plastic wrap and let stand for 15 minutes. Wipe off the baking sheet. Peel the poblanos and discard the skins. Make a 2-inch slit lengthwise in each poblano; do not remove the seeds or core.
Meanwhile, spread the tomatoes, árbol chiles, serrano, jalapeño and garlic on the same baking sheet. Broil, turning the vegetables occasionally, until blistered and blackened, 2 to 4 minutes for the árbol chiles; 8 to 10 minutes for the serrano, jalapeño and garlic; and 15 to 20 minutes for the tomatoes. Transfer the vegetables as they’re done to a food processor and let cool. Pulse a few times until combined but still chunky. Scrape the salsa into a medium bowl and season with salt.
In a small saucepan, combine the rice with 2/3 cup of water and bring to a boil. Add a generous pinch of salt. Cover and cook over low heat until the water is absorbed and the rice is tender, about 15 minutes. Remove the pan from the heat. Fluff the rice with a fork and fold in the Monterey Jack and Cotija cheeses. Using a small spoon, stuff the poblanos with the rice mixture.
In a stand mixer fitted with the whisk, beat the egg whites at high speed until soft peaks form, about 1 minute. Add the yolks and beat at high speed until the mixture doubles in size, about 5 minutes.
Set a wire rack on a baking sheet. In a large cast-iron skillet, heat 1/4 inch of oil until shimmering. Spread the flour in a shallow bowl. In batches of 2, dredge the poblanos in the flour and shake off the excess. Dip in the whipped eggs and fry over moderately high heat, turning once, until golden brown, 3 to 5 minutes. Transfer to the rack and season with salt. Serve immediately with the salsa.