Grease a 9-by-13-inch baking dish with 1 teaspoon oil. Heat the remaining tablespoon oil in a skillet over medium heat. Cook the diced pepper for 5–6 minutes, stirring, until softened. Add spinach and cook for 2–3 minutes until wilted and excess liquid has evaporated. Let cool briefly.

Whisk the eggs, milk, mustard, salt and pepper in a large bowl. Fold in the bread, cooked vegetables and two thirds of the cheese. Transfer to the prepared dish, distribute evenly, and sprinkle the remaining cheese on top.

Cover and refrigerate for 30 minutes so the bread absorbs the custard. For an overnight option, refrigerate promptly and bake within 24 hours. Preheat the oven to 350°F. Follow the baking-dish manufacturer's cold-to-hot guidance; use a suitable metal pan if baking directly from refrigeration.

Uncover and bake for 40–50 minutes, until puffed, golden and set in the center. Check several central spots with a food thermometer; an egg casserole without meat or poultry must reach at least 160°F. If the top browns too quickly, cover loosely with foil. An overnight-chilled casserole may need additional time.

Rest for 10 minutes, then cut into 8 portions. Refrigerate leftovers within 2 hours in shallow covered containers, use within 3–4 days, and reheat to 165°F. If the air temperature is above 90°F, refrigerate within 1 hour.