Preheat the oven to 350℉. Spray a 2 quart casserole dish with nonstick spray.
Heat a large skillet to medium, add butter or olive oil and saute the vegetables until somewhat softened.
Sprinkle the sautéed veggies onto the bottom of the casserole dish. Sprinkle the brie evenly over the top.
In a medium bowl, whisk together eggs, milk (or wine) and Dijon mustard. Pour over the vegetables in the dish. Sprinkle with salt and pepper.
Bake 45 to 55 minutes, or until the egg is cooked through. To check, use a knife to poke into the center. If you're seeing liquid, it needs more time in the oven. Slice and serve immediately.
Notes
I like to purchase the egg whites in the carton. They are easiest to measure, and you won't end up with a bunch of yolks and have to figure out what to do with them. Use remaining egg whites in the carton for scrambled eggs!
If you are preparing this recipe as GLUTEN-FREE, just be sure to use a brand of Dijon mustard that is known to be GF.