Place potatoes in a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low, cover, and simmer until tender, about 20 minutes. Drain; steam dry 1 to 2 minutes.

Heat 1/4 cup oil in a skillet over medium heat. Add onions; cook and stir until onions softened and translucent, about 5 minutes.

Combine potatoes and onions in a large bowl; season with 2 teaspoons salt, sugar, black pepper, and garlic. Mash until smooth; set aside.

Preheat the oven to 375 degrees F (190 degrees C). Line a baking sheet with parchment paper.

Beat warm water, remaining 1/2 cup oil, 2 eggs, and remaining 1 teaspoon salt together in a large bowl; gradually stir in flour. When dough has pulled together, turn it out onto a lightly floured surface and knead until smooth and elastic, about 8 minutes.

Divide dough into 3 even pieces; roll each piece out to about 9x13-inches, then cut each in half lengthwise. Divide and spread potato mixture down center of each dough strip. Roll each strip around filling; gently press to seal to make 6 logs.

Cut each log into 1-inch slices; place cut-sides down on the prepared baking sheet. Gently press edges of dough toward center of potato mixture to form a bun. Whisk 2 egg yolks and milk together in a small bowl; brush each knish with egg yolk mixture.