Preheat your oven to 375 degrees. Mix the eggs, milk, flour, salt, and pepper until smooth with an immersion blender.
Line a 15x10 rimmed baking sheet with parchment paper and spray the paper with non-stick cooking spray. Pour the batter on top of the parchment paper. Gently place the baking sheet in the oven.
While the omelet cooks, dice the onion, bell pepper, tomatoes, and ham or mushrooms. Pour olive oil into a hot skillet over medium high heat. Add the onion, bell pepper and ham, sauteing until the vegetables are tender. Stir in tomatoes and season to taste with salt and pepper.
After 20 to 25 minutes, the omelet will be puffed and browned very slightly on top. Remove it from the oven and allow the puff to deflate.
Sprinkle the omelet evenly with a layer of cheese and then the vegetable mixture, leaving about 2 inches on one side. Top the vegetable mixture with additional cheese, sprinkling all the way to the edge.
Using the parchment paper, roll the omelet gently together. If you wish to serve the omelet roll on a pretty platter, slide the parchment onto the platter before you completely roll the omelet off the paper.
Slice with a serrated knife and serve.