1. Lightly grease a 3-qt. oval baking pan. In a large bowl, whisk the eggs with the half-and-half, chiles, 2 teaspoons of salt and 1 teaspoon of pepper. Stir in the bagel pieces and let stand at room temperature for 20 minutes.
2. Meanwhile, in a large skillet, heat the 2 tablespoons of olive oil. Add the mushrooms and kale and season with salt and pepper. Cook over moderately high heat, stirring occasionally, about 7 minutes.
3. Stir in the cherry tomatoes, basil and rosemary and cook until the tomatoes start to soften, about 3 minutes. Remove the skillet from the heat and stir in the scallions; season with salt and pepper. Let cool slightly.
4. Fold the vegetables and shredded cheeses into the bagel mixture, then transfer to the prepared baking pan. Cover with plastic wrap and refrigerate for at least 4 hours or overnight.
5. Preheat the oven to 350 degrees. Remove the plastic wrap and cover the baking pan with foil. Bake for 40 minutes, remove the foil and bake for 45 minutes more, or until the top if puffed and golden and a toothpick inserted in the center comes out clean. Let stand for 20 minutes before serving.