Whisk together the flour, sugar, baking powder, and salt. Add the butter and cut it into the flour, using a pastry cutter or your hands until you have pieces that are about the size of a large pea.
Whisk together the egg, yolk, heavy cream, milk, and vanilla extract.
Pour the liquid over the flour/butter mixture and gently stir together with a spoon or rubber spatula. Don't stir too much, there will be lots of loose flour. Use a rubber spatula or your hands, gently fold the dough over itself several times, which will work in the flour and create a more cohesive dough. Stop just when the flour is mostly incorporated. See my Instagram video if it is unclear when to stop.
Lightly flour the work surface and dump out the biscuits. Press them into a circle about 3/4-inch-thick. Use a 3-inch round cutter to punch out the biscuits. If the cutter gets gloppy with dough, wash it clean, dry and dip it in flour.
Refrigerate the biscuits until ready to bake. They can be made hours before baking.