Mix the dry ingredients. In a medium bowl, whisk together the flour, baking powder, and salt.
Cream the butter and sugar, then add the egg and rose water. In the bowl of a stand mixer fitted with the paddle attachment, combine the butter and sugar. Beat on medium until light, fluffy, and doubled in volume, 3 to 5 minutes, using a rubber spatula to scrape down the bottom and sides of the bowl as necessary. Reduce the mixer to low, add the egg and rose water, and beat until just incorporated. Scrape down the bottom and sides of the bowl.
Add the dry ingredients. With the mixer on low, gradually add the dry ingredients and beat until just combined. Increase the mixer to medium-low and beat until the dough clumps around the paddle and/or sides of the bowl, 2 to 3 minutes.
Roll out the dough. Tip the dough out onto a piece of parchment paper around the size of a sheet pan and use your hands to shape it into a roughly 6-inch square. Place a second sheet of parchment over the dough, creating a parchment sandwich with the dough in the middle. Use a rolling pin to flatten the dough between the parchment sheets, working from left to right. Turn the dough 90 degrees and repeat every so often—doing so will help prevent the dough from cracking as you roll it. If the parchment starts to wrinkle and leave creases in the cookie dough, pull the sheet loose and smooth it before rolling the dough more. Continue rotating and rolling until you have a rough oval about 13 inches wide, 18 inches long, and between ⅛ and ¼ inch thick.
Chill the dough. Transfer the slab of cookie dough, still in between the parchment, to a sheet pan. Refrigerate for at least 1 hour to firm the dough.
Cut out the cookies. Once the dough is firm, remove from the refrigerator. Peel the top layer of parchment paper from the cookie dough slab and use the parchment to line a sheet pan. Line a second sheet pan with parchment as well. Use a 3-inch fluted cookie cutter to cut out shapes, and a smaller 1-inch fluted cookie cutter cut out a second circle with each cookie. Gather any cookie dough scraps, re-roll between two parchment paper sheets (with the instructions in step 4), and use the cookie cutters to stamp out shapes as many times as necessary to use all the dough. Place the cookies at least 1 ½ inches apart on the prepared sheet pans.
Freeze the cookies while preheating the oven. Freeze each sheet pan for 10 to 15 minutes to firm the cookies. While the sheet pans are in the freezer, position a rack in the center of the oven and preheat to 350°F.
Bake the cookies. Bake one pan at a time (keeping the pan in the refrigerator) for 10 minutes, or until the cookies are golden brown around the edges. Cool the cookies on the pan on a wire rack for 20 minutes, or until the edges and bottoms of the cookies are set and feel firm to the touch. Repeat to bake the remaining cookies. Cool completely before glazing.