Cut potatoes into large chunks and boil in water until soft. Drain and allow to cool.
Once cool, mash with 2 tablespoons oil, eggs, salt, pepper and dill. Stir in potato starch until thoroughly combined, and refrigerate the mixture for 1 hour.
Heat oil in a heavy non-stick pan over medium-high heat until shimmering.
Place 1/4 cup of batter at a time into the hot oil, using the back of a spatula to press flat until each pancake is no more than 1/4 to 1/3" thick. Cook until golden-brown on each side (2-3 minutes per side), flipping once.
Place on a paper towel lined plate to absorb excess oil. Serve while hot.