Chiles Rellenos Stuffed with Mexican Queso

MAKE THE SAUCE

1. Puree all sauce ingredients except oil with 1 ¼ teaspoons salt in a blender until smooth, then strain through a mesh sieve into a bowl, pressing on solids, then discarding them.
2. Heat oil in a deep heavy large skillet over medium heat until it shimmers.
3. Carefully pour in sauce and simmer gently, stirring occasionally, for about 10 minutes. (Sauce will still be thin).
4. Taste, and season with pepper, and more salt, if desired.
5. Set aside, but keep warm over low heat.

ROAST, STUFF AND FRY THE CHILES

1. Roast chilis on their sides over a gas flame over medium heat, turning with tongs, until skins are blistered and slightly charred, 4 - 6 minutes. (Or, broil on a rack about 2 inches from heat).
2. Transfer to a large bowl and cover with plastic wrap, let stand for 20 minutes. (This can be done ahead of time).
3. Carefully rub off skins from chilies, leaving stems attached.
4. Cut a slit lengthwise in each chile using kitchen shears or a sharp knife.
5. Carefully cut out the ribs and the seedpod. Clean out all seeds with a wet paper towel, if necessary (Leaving the seeds will make the peppers more hot).
6. Stuff chilies with cheese and enclose filling by overlapping slit slightly, then transfer to a plate. (All this can be done the day before).
7. Heat ½-inch of oil in another large heavy skillet over medium heat until it registers 350° F on a thermometer.
8. While oil heats, beat egg whites with ½ teaspoon salt, using an electric mixer until they just hold stiff peaks.
9. Whisk in the yolks, two at a time, just until incorporated.  Next, whisk in ¼ cup flour.  
10. Spread 1 cup of flour onto a plate. Generously dust chilies with the flour, coating all sides. Gently shake off excess flour. 
11. When oil is ready, dip chilies, 1 at a time into egg batter, spooning it over chile to cover completely.
12. Fry the chilis, turning once, until golden on all sides (Lap oil over any lighter areas, 4 to 5 minutes).
13. Transfer chilies with a slotted spoon to paper towels to drain. At this point, you can heat your oven to 300°F, place the chilies on a baking rack and then bake for 15 minutes. This will keep the chees nice an melty, crisp up the exterior, and render out a little more excess grease. Remove from oven.
14. Meanwhile, re-heat sauce.
15. Ladle sauce onto plates and place a chili on top of sauce.