Preheat oven to 375 degrees.
Sift the flour, 2 tablespoon sugar, the baking powder, and salt into the bowl of an electric mixer fitted with the paddle attachment. Blend in butter at the lowest speed and mix until the butter is the size of peas. Combine eggs, heavy cream, sour cream and vanilla extract and quickly add to the flour and butter mixture. Mix until just blended. The dough will be sticky.
Dump the dough out onto a well-floured surface. Flour your hands and pat the dough out to 3/4-inch thick. You should see lumps of butter in the dough.
Cut biscuits with a 3-4-inch cutter and place on a baking sheet lined with parchment.
Brush the tops with the egg wash. Sprinkle with sugar and bake 18-20 minutes, until the outsides are crisp and the insides are fully baked. Let cool on a wire rack.
Prepare the grill. Brush the peaches with melted butter. Cook peaches, flat side down, over direct medium heat, for 10 minutes. Rotate the peaches a quarter turn after three minutes, then turn them over once after 6 minutes of cooking. Remove the peaches from the grill and toss the in a bowl with the sugar, lemon juice and vanilla. Cover and keep warm until needed.
Split shortcakes in half, top each with a scoop of peach ice cream. Place a warm peach half on the ice cream and top with the remaining shortcakes half. Drizzle the syrup from the bowl with the peaches over each shortcake and serve immediately.
Yield: 6-8 servings