To a large pot of salted, boiling water, add the potatoes and cook until fork-tender, about 5 to 7 minutes. Use a slotted spoon to remove the potatoes and set aside.
Maintain the boil and add the broccoli. Let cook for a few seconds, up to a minute, until bright green. Drain and set aside.
In a large bowl, whisk together the eggs and milk until when the whisk is removed, no egg whites remain on the whisk. Season with salt and pepper, whisking to combine.
In a large, oven-safe skillet, heat the oil over medium heat until shimmering. Sautee the onion until softened and nearly translucent.
Add the potatoes and broccoli and cook for 1 minute.
Reduce the heat to medium-low and pour in the egg mixture. Let sit undisturbed until the egg along the edge of the skillet begins to set and is almost firm.
Top with the sliced tomatoes and sprinkle on the cheese.
Place under the broiler for 4 to 5 minutes until the center is firm when shaken. Serve warm.