Roast poblanos using your oven broiler on high and turning peppers frequently until most of the skin has blackened.
Remove peppers from oven and place them in a covered bowl to allow them to continue to steam so that you can remove the skin.
While the peppers are cooling, saute onions and tomatoes for a few minutes until they are translucent. Add garlic, salt and pepper and saute for another minute.
Remove onion mixture from heat and allow to cool.
Add cheeses to onion mixture and stir to evenly combine.
When peppers are cool enough to handle, gently remove the skin from the peppers. Make a lengthwise slit in the pepper and remove the seeds and membranes. (Don't make yourself crazy getting all of the seeds out. Just try to get out as many as you can. You can also skip this step, it will just change the texture of the cheese filling a bit and make the dish a bit more spicy.)
Gently insert the cheese mixture inside the cavity of the pepper, being careful not to make additional tears in the pepper. Secure the hole in the pepper with toothpicks to hold in the filling.
Using a stand or hand mixer, season the egg whites with salt and pepper and beat them until stiff peaks are formed.
Fold the egg yolks into the egg whites until combined.
Heat the vegetable oil in a frying pan or dutch oven. Use a thermometer to heat the oii to ~350 degrees.
Dredge the peppers in seasoned flour and gently shake off the excess flour, then coat them in the egg mixture.
Gently place the battered peppers in the hot oil and fry for ~2 minutes on each side until they are golden brown.
Remove the peppers from the oil and drain on paper towels.
Serve atop a bed of red or green enchilada sauce with rice, beans and hot sauce.