Peel 1 pound of the potatoes. Cut peeled potatoes into 1-inch pieces, and place in a medium saucepan. Add water and 2 teaspoons salt; bring to a boil over high. Reduce heat to medium-high; cook, undisturbed, until tender, 10 to 12 minutes. Drain, shaking off any excess water. Pass potatoes through a ricer into a large bowl. Let cool for 20 minutes.

Peel remaining 1 pound potatoes. Center a box grater on a clean kitchen towel, and shred potatoes on largest holes of box grater. Wrap grated potatoes in kitchen towel, and squeeze as much liquid from potatoes as possible. Transfer grated potatoes to bowl with riced potatoes. Stir in cheese, egg, chives, milk, pepper, and remaining 1 teaspoon salt until combined. Sprinkle flour over potato mixture, and stir until just combined.

Preheat oven to 250°F. Place a wire rack inside a baking sheet; set aside. Working in 3 batches, heat 1 ½ tablespoons butter in a large cast-iron skillet over medium until melted and bubbly; swirl to coat. Scoop 4 (scant ⅓-cup) portions of potato mixture into skillet; lightly flatten each pancake into a 3-inch round. Cook pancakes until golden brown on bottom, about 5 minutes per side. Reduce heat to medium-low, as needed, to prevent pancakes from overbrowning. Transfer pancakes to prepared baking sheet, and keep warm in oven until ready to serve. (Do not wipe skillet clean between batches.) Serve with sour cream.