Whisk the flour, baking powder, salt, and sugar together in a bowl. Using a fork, cut in the butter to coat the pieces with the flour. The mixture should look like coarse crumbs.
Fold the chocolate chips into the batter. Make a well in the center and pour in the half-and-half. Fold everything together just to incorporate; do not overwork the dough.
Turn the dough out on a lightly floured surface into a rectangle about 12 inches by 3 inches by 1 1/4 inches. Cut the rectangle in half length-wise, then cut in quarters length-wise, giving you 8 squares. Cut the squares in 1/2 on a diagonal to give you the classic triangle shape.
Place the scones on an ungreased cookie sheet and brush the tops with half-and-half. Bake for 15 to 20 minutes until beautiful and brown. Remove immediately from baking sheet and place on cooling racks.
While the scones are baking, make the glaze by combining confectioner's sugar with a small amount of water. Let the scones cool a bit before applying the glaze. Whisk the glaze to smooth out any lumps, and brush onto the surface of the scones. Sprinkle with turbinado sugar.