In the bowl of a stand mixer or a large bowl, sprinkle the yeast over the warm water along with the sugar. Stir to combine and allow to rest until frothy, 5-10 minutes.
Mix in 1 1/4 cups of the bread flour, cover with plastic, and allow to rest in the refrigerator overnight.
Mix in the remaining 1 1/4 cups flour and the salt. On a floured work surface, knead the dough until smooth and elastic.
Grease a round 9 inch ovenproof dish with oil. Divide the dough into 8 equal pieces. Form each piece into a ball and arrange in the oiled dish. Cover and allow to rest at room temperature until doubled and the rolls are touching.
Preheat oven to 425˚F (220˚C). In a small bowl, combine the 3 tablespoons oil, garlic, parsley, and salt. Set aside.
Once the pampushky have risen, brush with the beaten egg and bake until golden, 20-25 minutes. Immediately brush with the garlic oil and serve warm.