1. Filling: Stir together cream cheese and sugar with a wooden spoon until smooth. Add rose water and milk, and stir until smooth. Filling can be refrigerated in an airtight container up to 3 days; bring to room temperature and stir until smooth before using.

2. Cookies: Whisk to combine flour, cornstarch, and salt in a bowl. In a separate bowl, beat butter and confectioners' sugar with an electric mixer on medium-high speed until pale and fluffy, 3 to 4 minutes. Add rose water, and mix until combined, scraping down side of bowl. Reduce speed to low and add flour mixture; mix until just combined. Divide dough in half, and shape into disks. Wrap each in plastic, and chill 1 hour.

3. Preheat oven to 350 degrees. On parchment, roll 1 disk of dough to 1/8-inch thickness; chill 15 minutes. Cut 1 1/2-inch rounds from dough, and place 1 inch apart on parchment-lined baking sheets. Repeat with remaining disk. Using the wide end of a pastry tip, cut a 1/2-inch hole off-center in half the rounds. Bake, rotating sheets halfway through, until barely golden, about 14 minutes. Transfer cookies to wire racks to cool completely. (Unfilled cookies can be stored in an airtight container up to 3 days.)

4. Dust cut-out cookies lightly with confectioners' sugar. Spread a heaping 1/2 teaspoon filling on whole cookies and top with cut-out cookies. Place a candied rose petal or violet in each hole. Once sandwiched, cookies can be stored in a single layer in an airtight container at room temperature up to 1 day.