Measure 16 ounces powdered sugar (4 cups; 450g) and place in the bowl of a stand mixer, then add egg whites, rum, vanilla, salt, and cream of tartar. Stir with a flexible spatula to form a smooth paste, then set over a gently simmering water bath in a 3-quart saucier and stir until paste is hot to the touch, or about 150°F (66°C) on an instant-read thermometer
Transfer to stand mixer fitted with a paddle attachment, add remaining 2 ounces powdered sugar (1/2 cup; 60g), and mix at low speed to combine. Increase speed to medium and beat until thick and frosting-like, about 20 seconds or until the mixing bowl feels cool to the touch. Use immediately as a thick frosting or to make chunky decorations, like the buttons on a gingerbread man or little rosettes on a cake
To Thin the Icing: Reduce speed to low, add cream, and continue mixing until smooth. Remove bowl from mixer and lift paddle attachment, moving it in a figure 8 pattern as icing streams back into bowl. If the figure 8 disappears in exactly 8 seconds, the icing is ready to use as a cookie glaze. If it melts away faster, thicken by adding a spoonful of powdered sugar. If it takes longer than 8 seconds to disappear, thin by adding a few drops of cream. Repeat this test, making adjustments as you go, until the figure 8 takes exactly 8 seconds to disappear
To Color the Icing, if Desired: Divide icing among several small bowls, one for each color you'd like to prepare. Cover each with plastic wrap pressed directly against the surface. Working with one bowl at a time, stir in a few drops of gel paste. When your desired color has been achieved, immediately transfer to a disposable pastry bag fitted with a #3 pastry tip, or a parchment cone (for ease of use, I like to stand the bag/cone upright in a small drinking glass)