After roasting and peeling the chiles, carefully slit the bottom half of the chiles or for a milder chile relleno remove the stems and pull out the membranes and seeds being careful not to tear the chiles. Fill each chile with some cheese and set aside.
On a plate combine flour, 1⁄2 teaspoon salt, and 1⁄2 teaspoon black pepper. Place the filled chiles in the flour and coat all sides well. Shake off any excess flour. Reserve.
Using a stand mixer or an electric hand mixer beat the egg whites and cream of tartar, 2 teaspoons salt, and 1⁄2 teaspoon pepper on high speed until soft peaks form.
Add in the egg yolks, and carefully fold the egg yolks into the egg whites being careful not to mix too much so the egg whites don’t fall.
Fill a large heavy-bottomed saucepan about a third of the way up with canola oil and heat on medium-high heat. You want to get the oil very hot before frying your chile rellenos. Test the oil by dropping some of the egg white mixture into the oil. If the mixture sizzles and floats to the top, it’s the right temperature. If it sinks, the oil is not hot enough.
Dip the filled and flour-dusted chiles into the egg mixture until well coated, forming a little cocoon. Coat each chile one at a time just prior to frying. Carefully place the egg-coated chile rellenos in the hot oil, about 2 at a time. Fry until golden brown, turning once. Drain on paper towels. Change paper towels 2 to 3 times to absorb excess oil.
Arrange the chiles rellenos on a serving platter and drizzle each with some warm ranchero sauce and serve.