Preheat oven to 400°F.

Place potatoes and 1 ½ teaspoons salt in a small saucepan; add enough cold water to cover potatoes by 1 inch. Bring to a boil over high; boil, undisturbed, until tender when pierced with a knife, 15 to 20 minutes. Drain well; let stand until cool enough to handle, 10 to 15 minutes.

Meanwhile, cook bacon in a large skillet over medium, flipping as needed, until crisp, 8 to 10 minutes; transfer bacon to a paper towel–lined plate. Discard bacon drippings, or reserve for another use. Do not wipe skillet clean.

Heat oil in same skillet over medium. Add onion; cook, stirring often, until softened and deep golden brown, 10 to 15 minutes. Transfer onion to a small bowl; sprinkle with pepper and remaining ¼ teaspoon salt, stirring to combine. Set aside.

Peel potatoes, and thinly slice crosswise; set aside. Cut bacon slices crosswise into thirds; set aside.

Line a large baking sheet with parchment paper. Unfold puff pastry sheet onto prepared baking sheet into a 14- x 10-inch rectangle about ⅛ inch thick. Lightly score a ½-inch border around the pastry; prick the pastry inside the border all over using a fork. Bake until pastry is puffed and lightly golden, about 20 minutes. Deflate the pastry inside scored border using the back of a fork.

Top pastry evenly with half of the cheese, bacon, half of the onion, and potatoes. Top evenly with remaining onion and remaining cheese. Bake at 400°F until cheese is melted and pastry is browned, 10 to 12 minutes.

Let stand 1 to 2 minutes before cutting into 6 pieces. Garnish with thyme and additional pepper, and serve.