Position a rack in the center of the oven and heat the oven to 425°F. Line a large heavy-duty baking sheet with parchment.
Sift the flour, ⅓ cup of the sugar, the baking powder, and baking soda into a large bowl. Stir in the salt. Using a pastry blender, a fork, or your fingertips, work the butter into the dry ingredients until the mixture resembles coarse cornmeal.
In a small bowl, beat the egg and heavy cream with a fork. Mix in the buttermilk. Make a well in the center of the flour mixture and pour in the cream mixture. Mix with the fork until the dough is evenly moistened and just comes together; it will still look a little shaggy.
Gather the dough and gently knead it three or four times. If the dough seems dry and doesn’t form a cohesive mass, work in more cream, 1 tsp. at a time.
Transfer the dough to a lightly floured surface and roll it into a ¾ -inch-thick disk. With a sharp 2½-inch biscuit cutter, press straight down to cut the dough into rounds and lift straight up to remove (don’t twist the cutter or it will seal the sides of the biscuits and interfere with rising).
Transfer the rounds to the prepared baking sheet. Gather the dough scraps, gently knead them together, re-roll, and cut out more biscuits until you have a total of 6.
Lightly brush the biscuit tops with cream (about 1 Tbs.) and sprinkle with the remaining 1 Tbs. sugar.
Bake, rotating the baking sheet once, until the biscuit tops are lightly browned, 10 to 15 minutes. Let the biscuits cool slightly while you whip the cream.