In a large bowl, combine the flour, baking powder, granulated sugar, salt, and lemon zest. Stir to combine thoroughly.
Add the cold diced butter to the flour mixture and work it in with your fingers, forks, or a pastry cutter. The mixture should have some crumbs the size of small peas.
In a medium bowl, combine the half-and-half, egg, vanilla extract, and lemon extract, if using. Whisk to blend.
Add the egg mixture to the dry mixture and work it in until the ingredients are moistened. Avoid overworking.
Turn the dough out onto a floured surface and knead just a few times to form a soft dough. Pat the dough into a circle or square about 1/2-inch thick and cut out scones with a biscuit cutter. Alternatively, use a knife to cut the dough into triangles or squares.
Arrange the unbaked scones on the prepared baking sheet and refrigerate them for at least 20 minutes.
Preheat the oven to 375 F.
Bake the scones for about 15 to 18 minutes, until lightly browned.
Meanwhile, combine the glaze ingredients in a small bowl. Whisk until smooth. It should be thin enough to brush over the scones.
Remove the scones to a rack and brush the glaze over the hot scones. Brush with the glaze a second time after the scones have cooled.