Boil the potatoes in a large pot of salted water until partly tender (a paring knife will meet resistance only in the very center), 12 to 15 minutes. Let cool slightly. Gently crush each potato to flatten slightly.
Heat the oil in a large skillet over medium-high heat. Cook the potatoes until browned and crisp, 4 to 5 minutes per side. Season with salt and pepper.
Top the potatoes with the sour cream, smoked salmon, dill, and flaky sea salt.