Preheat oven to 400°F. Bring potatoes, 2 tablespoons of the salt, and enough water to cover by 1-inch in a medium saucepan to a boil over high, undisturbed. Reduce heat to medium; cook, undisturbed, until potatoes are very fork tender, about 25 minutes. Drain well.
While potatoes are coming to a boil, cook bacon in a large nonstick skillet over medium-high, stirring occasionally, until crisp, 10 to 12 minutes. Using a slotted spoon, transfer bacon to a paper towel lined plate; set bacon aside. Reserve 2 tablespoons bacon drippings, discard or reserve remaining drippings for another use. Do not wipe skillet clean. Heat 1 tablespoon of the reserved drippings in same skillet over medium-high; add onion to reserved drippings; cook, stirring occasionally, until tender, about 3 minutes. Add arugula, thyme, and 1/4 teaspoon of the salt; cook, stirring constantly, until wilted, about 1 minute. Remove from heat; set aside.
Brush a 9-inch round cake pan with remaining 1 tablespoon bacon drippings. Place drained potatoes in an even layer; using a flat bottom measuring cup, press potatoes firmly into the bottom and about 1-inch up the sides of the cake pan. Sprinkle 1 cup of the cheese and half of the cooked bacon (about 1/2 cup) in an even layer over bottom of potato crust. Place onion-arugula mixture in even layer over cheese, sprinkle with remaining 1 cup cheese and cooked bacon (about 1/2 cup); set aside.
Whisk together eggs, cream, and remaining 1 teaspoon salt in a large bowl until frothy, about 30 seconds. Pour egg mixture over filling pie plate. Carefully transfer to oven. Bake in preheated oven until filling is set and an instant-read thermometer registers 160°F, about 25 minutes. Let cool slightly on wire rack, about 15 minutes. Garnish with thyme and pepper.
