Preheat oven to 325° F.
Cream butter until light, fluffy, and very soft - it should be the consistency of mayonnaise. Add salt and rosewater and stir to combine well.
Add rose sugar and powdered sugar; cream with butter until thoroughly combined.
Sift together flour and cornstarch; stir into butter mixture just until combined.
Roll dough out between two sheets of parchment paper to about 1/4" inch thickness. Do NOT add flour – it will make the final texture of your cookies tough.
Chill dough until firm, about 20 minutes.
Cut out desired shapes. You can use a cookie cutter, biscuit cutter, or a fluted pastry wheel, like I did here. Re-roll any leftover dough scraps to cut more cookies as needed, but try to minimize re-rolling and shaping dough, as it will get tougher the more you work it.
Chill cut cookies again until firm, about 20 minutes. Preheat oven to 325° F while chilling.
Bake until cookies are just starting to brown at the edges; middle should still be light, about 12-15 minutes. Adjust cooking time if necessary, depending on cookie size (see notes).
While still slightly warm, sprinkle superfine sugar over the top of the shortbread cookies.