Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 9-inch cake pan.
Cream sugar and butter for cake together in a bowl with an electric mixer. Beat in eggs, one at a time, then stir in vanilla extract. Combine flour, baking powder, and salt separately, then add to mix, and cream together. Stir in half-and-half and rose water. Add a few drops of food coloring to turn pinkish (or whatever color you want). Pour into the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center of the cake comes out clean, 30 to 40 minutes. Cool on a wire rack for 5 minutes. Run a table knife around the edges to loosen. Invert carefully onto a serving plate or cooling rack. Let cool, about 30 minutes.
While cake cools, beat confectioners’ sugar and butter with an electric mixer on low speed, then increase speed to medium for about 3 minutes. Add half-and-half and vanilla extract and beat for 1 minute more. Add more half-and-half if frosting is too thick. Frost cooled cake.