Peel and dice the potatoes. Add the potatoes to a large pot along with a generous pinch of salt. Place over high heat and bring to a boil. Cook the potatoes for 15 to 20 minutes until tender.
When the potatoes are tender, drain and return to the pot. Mash the potatoes then transfer to a mixing bowl and allow to cool completely. To cool the potatoes quickly, spread them out on a plate and refrigerate until chilled. You should have 3 cups of mashed potatoes.
Transfer the cold mashed potatoes to a mixing bowl. Add the beaten eggs and stir into the potatoes. Add the flour, kosher salt, and pepper and mix until combined. Stir in the chopped green onions. Batter will be thick.
Place a rack on a baking sheet and have ready to drain the potato cakes. In a wide skillet, add enough vegetable oil to cover the bottom of the pan, about 1/8 inch deep. Place over medium heat.
Drop a spoonful of the batter into the hot oil. Gently spread the batter out to create a flat cake, about 2 inches in diameter. Alternatively, use lightly oiled hands to shape spoonfuls of the batter into flat discs. Add 4 or 5 more to the pan. Allow the cakes to fry until the bottoms are golden brown – about 3 to 4 minutes.
Carefully flip the cakes over and cook for another couple of minutes until browned on the other side. Transfer the potato cakes to the rack to drain. Repeat with the remaining batter until all the potato cakes are cooked.
In a small bowl, combine the sour cream, chopped chives, kosher salt, and pepper. Stir together. Refrigerate until ready to serve.
To serve, arrange the potato cakes on a serving platter, topping each one with a spoonful of the sour cream mixture. Shape thin slices of smoked salmon into rosettes and place on top of the cakes. Garnish with a dollop of pickled mustard seeds and fresh chopped chives. Enjoy!
Notes
*Recipe for Pickled Mustard Seeds can be found here