How to Make It
Preheat oven to 400°F. Place potatoes in a large bowl, and rinse under cold water, agitating with your hands until water runs clear. Working in batches, pat potatoes dry with a clean kitchen towel. Place potatoes in a colander, and toss with salt. Let stand 10 minutes. Working in batches, pat dry again with a clean kitchen towel until potatoes no longer glisten with water.
Heat 1 teaspoon oil in a medium stainless steel or cast-iron skillet over high until it begins to smoke. Reduce heat to low; pour out oil, and wipe out skillet with a paper towel. (This process will help keep the potatoes from sticking.) Increase heat to medium, and add 1/4 cup oil.
When oil is very hot and begins to shimmer, quickly pull skillet off heat, and carefully add potatoes in an even layer. Return skillet to heat over medium. Using a metal or heat-resistant spatula, loosen potatoes from sides of pan, and press down in center to form a cake.
Pour remaining 1/4 cup oil around and down sides of potato cake. Cook until bottom is slightly crisp and lightly browned, 7 to 8 minutes, giving skillet a quarter turn every 2 minutes to ensure even browning.
Slide rösti onto a large plate. Place a second large plate on top, and invert. Slide rösti back into skillet. Cook until bottom is slightly crisp and browned, 7 to 8 minutes, giving skillet a quarter turn every 2 minutes. Slide rösti onto a wire rack set inside a rimmed baking sheet. Bake in preheated oven until crispy and browned and excess oil has pooled in baking sheet, 8 to 10 minutes.
Remove from oven, and let cool until slightly firm, about 5 minutes. Using a spatula, gently slide rösti onto a large plate. Top with crème fraîche, pastrami, chives, dill, mustard, and pickle slices.