Preheat oven to 350 degrees. Line two baking sheets with parchment paper.
In a large mixing bowl, stir together the flour, sugar, baking powder, and salt until combined. Using a pastry blender, cut the cold butter into the flour mixture until it resembled crumbs. In a smaller bowl, whisk together the egg, half-and-half, rosemary, and lemon zest. Pour it into the flour and butter mixture and stir together until a shaggy dough forms. Turn the dough out onto a lightly floured work surface and work together with your hands until it just holds together, being careful not to overwork it. Pat the dough into a large rectangle, about an inch thick. Using a sharp knife or a bench scraper, cut the dough into 12 squares. Then, cut the squares in half diagonally to form smaller triangles. These will puff up substantially while baking due to the baking powder in the dough, so be sure to space them out on the two prepared baking sheets. Bake the scones for 18-20 minutes, or until golden and set. Allow the scones to cool on a wire rack while you prepare the glaze.
For the glaze: whisk together the powdered sugar, half-and-half, lemon zest, lemon juice, and rosemary until smooth. When the scones have cooled at least 15 minutes, dip the top of each scone directly into the glaze. Return the scones to the wire rack to allow the glaze to set.