Step 1In a large saucepan over medium heat, heat the oil. Stir in the garlic, oregano, onion, vinegar, bell pepper, tomatoes (and their juice), chiles and broth. Increase the heat and bring to a boil. Cook for 2 minutes, then stir in the black pepper, bay leaves and salt to taste.
Step 2Reduce the heat to a gentle simmer and continue to cook, stirring frequently, until the vegetables have softened and the tomatoes start to break apart, about 25 minutes.
Step 3Remove from heat, discard the bay leaves, and mash the tomatoes with a potato masher or whisk until you have a coarse sauce. Season again to taste. Set aside in a warm place.
Step 1Divide the cheese into 6 mounds and roll each mound into a football-shaped ball with your hands. Slit each chile lengthwise halfway and gently stuff a ball of cheese into each. Set aside.
Step 2In the bowl of a stand mixer, or in a large bowl with a hand mixer, beat the egg whites until stiff peaks form, 4 to 6 minutes. In a separate bowl, beat the egg yolks until frothy. Gently fold the yolks into the whites to complete your egg batter.
Step 3In a large skillet or frying pan, add enough oil to come up the sides by one-half inch. Heat the oil until a thermometer inserted reads 350 degrees.
Step 4Gently spoon a little egg batter into the pan, spreading it so it is roughly the dimensions of one side of a stuffed chile. As soon as the batter begins to set, 1 to 2 minutes, lay a chile over the top, then spread an equivalent amount of batter over the chile.
Step 5Turn over the chile relleno and fry an additional 1 to 2 minutes until golden on all sides. Remove the chile relleno with a slotted spatula or spoon, and place on a warm plate. Repeat until you have 6 chiles rellenos.
Step 6Spoon one-half cup sauce over each chile relleno and serve immediately.