Heat a dry 10" skillet over medim heat for 2 minutes. Toast the ancho and pasilla chiles in the heated skillet for about 20 seconds on each side. They'll become fragrant, but do not allow them to scorch or they'll become bitter. Remove the stems, seeds and ribs from the toasted chiles, and soak them in hot water to cover for about 20 minutes to rehydrate. Drain them and put them in the blender with the chipotle chile.
Heat 1 tbs of oil over medium heat in the same skillet you used for toasting the chiles. Add the onions. Cook until soft and golden brown, stirring often, for about 10 minutes (lower the heat if needed to prevent scorching). Add the garlic and cook, stirring, for an additional minute. Move the onions and garlic to the blender, along with the cilantro, brandy, and 1/4 cup water. Puree everything to a smooth paste, adding more water as needed, 1 tbs at a time. Transfer the chile puree into a small bowl.
Heat the remaining 2 tbs of oil in a small saucepan over medium-high heat. Make sure you're wearing an apron or smock at this point (trust me). When the oil is shimmery and just beginning to smoke, quickly add the chile paste (step back a bit, it will spatter violently).Cook, stirring constantly to incorporate the oil, for about 2 to 4 minutes, or until the mixture becomes very thick. Turn down the heat a bit if necessary to prevent scorching. Reduce the heat to medium and add the broth gradually, stirring. Add the brown sugar and salt. Simmer for another 1 to 2 minutes, or until the mixture has the consistency of a medium-thick sauce. Add salt to taste.
Place your oven rack 4" from the broiler element and heat broiler on high. Drizzle both sides of your steaks with lime juice and season with salt and pepper to taste. Heat an 11 or 12" skillet (cast iron is ideal here) over medium-high heat. Add the olive oil. Sear the steaks, two at a time, for two minutes per side. Lower the heat as needed, and continue cooking steaks until they are done to your liking (approximately 2 additional minutes on the second side for medium rare). Transfer the first two steaks to a rimmed baking sheet and repeat with remaining 2 steaks.
Once all the steaks are cooked, turn the heat to medium and pour the chile sauce into the pan. Stir to incorporate any browned bits and drippings into the sauce. Sprinkle the steaks with the Oaxaca cheese, spoon some sauce over them, then top with the cotija. Put the baking sheet under the broiler for about a minute, just to melt the cheese. Serve immediately.