Step 1Heat oil in large nonstick skillet over medium-high heat. When hot, add peppers and onion. Cook until softened, stirring often, about 10 minutes. Drain liquid from 2 tablespoons salsa and stir in. Remove from heat.
Step 2Place chopped cilantro, eggs, milk, salt and pepper to taste in large bowl. Whisk until mixed well.
Step 3To assemble, fit single layer of bread tightly together in bottom of greased 8-inch-square baking pan, or other shallow 7-cup baking pan. Spread half the vegetables over bread, then sprinkle with half the cheese. Cover with remaining bread slices in single layer, tightly fitting them into pan. Repeat layering of vegetables and cheese.
Step 4Pour egg mixture evenly over surface of strata. Use spatula to gently press top layer of bread down into liquid. Refrigerate at least 6 hours or overnight, covered with plastic wrap. Before baking, remove wrap; use spatula once more to gently press top layer of bread down into liquid.
Step 5Bake at 350 degrees until puffy and golden, 35 to 45 minutes. Let rest 10 minutes before serving. To serve, garnish strata with cilantro leaves, cut into squares or wedges; pass salsa separately. (Leftover strata can be reheated, covered with foil, in 350-degree oven for 30 to 40 minutes.)