In a large pan, sauté the broccoli, peppers, and onion in a little oil until the broccoli is fork-tender and the onion is translucent, about 5-10 minutes. Turn off the heat and allow it to cool for a few minutes until it is closer to room temperature.

Meanwhile, beat together the eggs, mustard, and spices. Dip 2 slices of the bread in the egg, coating both sides. Place bread side by side in a 8x8-inch baking dish--it should basically cover the whole bottom, it's okay if it doesn't quite or if it goes up the sides a bit. Sprinkle the gruyere over the bread in an even layer. Spoon in the broccoli mixture so it evenly covers the bread. Set aside.

Whisk the cream into the remaining seasoned eggs. Pour over the broccoli mixture. Top with the cheddar. Crumble up the remaining bread over the top. If your bread is really not crumbly (I find rye bread crumbles pretty easily), you could toast it and then run it in the food processor or blender to make crumbs. I didn't feel the need to do any of that and left it kind of "rustic".

Bake the dish until bubbly and fully cooked, about 40 minutes. It is a little hard to tell because the dish stays fairly pale but the middle shouldn't be jiggly and nothing should look runny. You can stick a knife or toothpick in the middle--it should come out with some melted cheese but you don't want raw egg or any drips.

Allow it to sit for a couple of minutes and then scoop or slice it and serve.