Makes 8 large rolls
Heat milk and 1 tablespoon sugar in a small glass in a microwave until it reaches 110 to 115 degrees, about 30 seconds. Transfer warmed milk to a large bowl and add yeast; let it bloom for 5 to 10 minutes.
Dab a paper towel in vegetable oil and lightly grease the inside of another large mixing bowl. Add flour, 3 tablespoons sugar, salt, butter, and two whisked eggs to yeast mixture and, using a wooden spoon, stir to blend well. When dough begins to clump, add potato, stirring until it comes together to form a mass. Transfer dough to a lightly floured work surface and knead until it comes together and is smooth and springy, 2 to 3 minutes (dust your hands and work station with flour as necessary for easier handling). Transfer to the greased bowl. Lightly brush dough with oil, cover with plastic wrap, and let sit in a warm place until it doubles in size and small bubbles appear on the surface, about 1 1/2 hours (times will vary depending on room temperature).
Lightly grease two baking sheets with oil.
Generously dust a work station with flour. Dough will be sticky; dust your hands as necessary. Punch down dough by gently flattening it with the heel of your hand, forming it into a roughly rectangular shape. Using a bench scraper or knife, cut dough into 8 even portions about 3 1/2 ounces each. Shape each piece into rounds by slightly cupping a hand over dough and making a circular motion on the counter (the dough may get sticky; dust with a little flour mas needed). After shaping, place rolls, seam side down, onto prepared baking sheet; staggering with about 2 inches of space in between each. Brush rolls lightly with oil. Cover loosely with a plastic bag (a clean see-through garbage bag will suffice) and let dough rise until doubled in size, about 1 hour (times will vary depending on temperature).
Preheat oven to 375 degrees.
Whisk remaining egg and heavy cream together. Brush rolls with egg mixture and transfer to oven. Bake until golden brown and cooked through, 20 to 25 minutes. Remove from oven and transfer baking sheet to a wire rack to cool.