Preheat the oven to 400 degrees F.
To prep the butter, using a box grater, shred the butter into a pile of shavings, and keep in the freezer while you get the rest of the ingredients going. If you don't have a box grater, a fine dice works fine too.
In the bowl of an electric mixer fitted with a paddle attachment, combine the 4 cups of flour, 3 tablespoons sugar, baking powder, and 1 teaspoon salt. Add the butter and mix on the lowest speed until it is well incorporated. Whisk together the eggs and heavy cream and, with the mixer on low, quickly add them to the flour-and-butter mixture, combining just until blended. Toss the chocolate chips with the 1 tablespoon flour, add them to the dough, and mix quickly to distribute the chips through the dough. The dough may be a quite sticky.
Dump the dough out onto a well-floured surface and knead quickly to be sure the ingredients are combined. Flour your hands and a rolling pin and roll the dough 3/4-inch thick. You should see lumps of butter in the dough. Cut with a 3-inch plain round cutter and place the circles on two sheet pans lined with parchment paper.
Brush the tops of the dough with egg wash. Sprinkle with sugar and bake for 20 to 25 minutes, until the tops are browned and the insides are fully baked. Serve warm.