Heat oil in a large frying pan over medium-high heat. Add chiles and onion and season with salt and pepper. Cook, stirring ocassionally, until tender and starting to brown. Remove from heat and scrape into a large bowl.
Butter a 13-by-9-inch baking dish and set aside. Add the bread, sour cream, salsa, and cilantro to the chile mixture and stir until everything is coated in sour cream. Transfer mixture to the baking dish and spread into an even layer.
Whisk together eggs, half-and-half, salt, cumin, and black pepper in a separate large bowl until well combined. Pour over bread, cover and refrigerate overnight.
Heat oven to 350°F. Remove strata from refrigerator about 20 to 30 minutes before you plan on baking it. Sprinkle cheese over the top and bake, uncovered, until strata is puffed, golden brown and set in the center, about 50 to 60 minutes. Serve hot with more salsa if desired.