In the bowl of a stand mixer fitted with a paddle attachment (or using a hand mixer), cream together softened butter and sugar until smooth. Mix in rose water and vanilla extract.
Whisk together flour and salt. Add dry mixture to creamed butter. Mix until there are no longer any dry streaks of flour. Dough will be slightly dry and a bit crumbly.
Wrap dough in plastic wrap and let chill in the fridge for 1 hour (up to overnight).
Preheat oven to 350 degrees F. Allow dough to rest at room temperature for 10-15 minutes to soften. Roll dough out on a lightly floured work surface to a thickness of 1/4-inch. Stamp out rounds using a 2-inch fluted circle cutter. Gather dough scraps and press together to roll out additional cookies. Place cookies on a parchment lined baking sheet, spacing cookies about 1-inch apart.
Bake for 18-20 minutes until the edges of the cookies are golden brown. Allow cookies to cool on baking sheet.