Preheat oven to 400°F; position rack in lower third of oven. Combine potatoes, 2 tablespoons salt, and enough cold water to cover by 1-inch in a large saucepan; bring to a boil over high. Reduce heat to medium; cook, undisturbed, until potatoes are fork-tender, 15 to 20 minutes. Drain well and pat dry.

While potatoes are boiling, cook bacon in a 10-inch cast-iron skillet over medium-high, stirring occasionally, until crisp, about 15 minutes. Using a slotted spoon, transfer bacon to a paper towel-lined plate; set bacon aside. Measure 3 tablespoons bacon drippings; discard or reserve remaining drippings for another use. Brush 2 tablespoons of the bacon drippings over bottom and sides of skillet; set aside.

Place drained potatoes in an even layer in prepared skillet; using a flat bottom measuring cup, smash potatoes firmly into bottom, then press over bottom and about 1 ½-inches up sides of skillet. Use a spoon or small offset spatula to evenly spread potatoes, smoothing and patching any holes or thin spots as needed. Brush potato crust evenly with remaining 1 tablespoon bacon drippings and sprinkle evenly with ½ teaspoon salt. Bake the potato crust until edges are golden brown and slightly crisp and center is lightly golden, 35 to 40 minutes.

Remove skillet from oven. Sprinkle half of the Gruyère (about ¾ cup) and half of the Parmesan (about ¼ cup) in an even layer over bottom of potato crust. Top evenly with ¾ cup cooked bacon. Sprinkle with remaining half of Gruyère and Parmesan; set aside.

Whisk together eggs, cream, dry mustard, and remaining 1 teaspoon salt in a medium bowl until well combined. Pour egg mixture over filling in skillet, spreading into an even layer, if needed. Carefully transfer to oven.

Bake at 400°F until filling is set, and a paring knife inserted in center comes out clean, 20 to 25 minutes, loosely covering edges with aluminum foil to prevent over-browning, if needed. Let cool slightly on a wire rack before serving, about 20 minutes. Sprinkle with remaining cooked bacon (about ½ cup) and garnish with pepper.