Arrange a rack in the top third of the oven and heat the oven to 350°F.

Thinly slice 6 ounces baby potatoes into rounds. Cut 3 thick-cut bacon slices crosswise into small pieces. Finely slice the green and white parts of 2 medium scallions on a slight diagonal. Grate 3 ounces sharp cheddar cheese on the large holes of a box grater (about ⅔ cup).

Whisk 8 large eggs in a large bowl. Add ¼ cup half-and-half or whole milk, ½ teaspoon kosher salt, ¼ teaspoon black pepper, and ¼ teaspoon dry mustard or 1 teaspoon Dijon mustard. Whisk to combine.

Place the bacon in a 10-inch cast iron or oven-safe nonstick skillet over medium heat and cook until crispy, about 7 minutes. Using a slotted spoon, transfer the bacon to a medium bowl. Add the potatoes to the pan, spread into a single layer, and cook for 3 minutes.

Add ½ cup water. Cover, reduce the heat to medium-low, and cook the potatoes until slightly softened, 3 to 5 minutes. Using the slotted spoon, transfer the potatoes to the bowl with the bacon. Pour off any remaining water and dry the pan.

Add 1 tablespoon canola oil to the pan and return to medium-low heat. Pour in half the egg mixture and let cook undisturbed until the bottom begins to set, about 3 minutes.

Sprinkle with half of the bacon and potato mixture, half the scallions, and half the cheese. Pour the remaining egg mixture on top and shake the skillet to settle the mixture. Sprinkle with the remaining potato and bacon and scallions. Shake the skillet again, then sprinkle with the remaining cheese. Cook undisturbed until the eggs at the edges of the skillet begin to set, about 2 minutes.

Transfer the skillet to the oven and bake until the eggs are just set and the edges are golden-brown and come away from the pan, about 15 minutes. (The center should no longer jiggle.)

Heat the broiler to HIGH and broil until the top of the frittata is lightly golden-brown in spots, 1 to 2 minutes. Let cool in the skillet for 5 minutes, then slice into wedges and serve warm or at room temperature.