Preheat the oven to 400°F.

In a medium sauce pan, add the potatoes and cover with water. Bring to a boil, add 1 teaspoon of kosher salt and cook until the potatoes are fork tender, about 6-8 minutes. Drain the water and set the potatoes aside.

While the potatoes are cooking, add the bacon to a large skillet over medium-high heat and cook until the bacon is crisped, stirring often, about 6-8 minutes. Use a slotted spoon to transfer the cooked bacon to a plate lined with a paper towel, leaving the bacon renderings in the pan. Add the chopped broccoli and the onion to the bacon renderings and cook over medium heat until softened, 3-4 minutes, then add the potatoes and bacon to the skillet, stir, and cook for 2-3 more minutes.

Whisk the eggs and milk in a 4-cup measuring cup, and season with kosher salt and freshly ground black pepper. Top the potatoes and broccoli mixture with the shredded cheese and then pour the egg mixture evenly over the cheese. Cook the eggs lifting the edges of the eggs as they cook so that the egg mixture flows under the cooked portion and the egg is almost set. Place the skillet in the oven and cook for 20-25 minutes or until the egg is puffy and completely set. Slice and serve warm or at room temperature.