Beat eggs and water thoroughly, until eggs begin to turn a lemony color.
Butter (or oil) a casserole dish, or individual oven-proof bowls. Add cheeses, then sauted vegetables. Then the broccoli. Finally, arrange the tomato slices over the vegetables and cheese. The tomatoes will float slightly as the omelet bakes, so place them with an eye toward a nice presentation.
Put the casserole dish(es) on a baking sheet. Put the sheet on the extended oven rack, and then pour in the egg mixture. This saves having to attempt to get the full dishes into the oven without spilling egg.
Bake approximately half an hour at 325 degrees. If you are making individual omelets, they'll cook a little faster. Using a deep casserole dish will take a little longer. The dish is done when it puffs, and the middle doesn't move when slightly shaken. Note that the tomatoes will leave a bit of liquid on top of the dish - that's fine.