Prepare the ashta first.
In a saucepan, whisk together the milk, heavy cream, cornstarch, and sugar until smooth.
Place over medium-low heat and whisk constantly until thickened. Once it begins bubbling, cook gently for about 1 minute while whisking, then remove from the heat. Stir in the rose water.
Transfer to a shallow bowl and press plastic wrap directly onto the surface. Refrigerate for at least 3 hours, until completely cold and set.
Make the syrup.
Combine the water, sugar, and optional cinnamon stick in a saucepan. Heat, stirring until the sugar dissolves.
Bring to a boil, reduce the heat, and simmer for 5 minutes without stirring. Remove from the heat, add the lemon juice, and let cool completely. Remove the cinnamon stick before serving.
Cook the semolina dough.
In a pot over medium heat, combine the water and sugar. Stir until dissolved.
Gradually add the fine semolina, stirring constantly to prevent lumps. Continue cooking until it thickens into a smooth paste.
Add the cheese and rose water.
Reduce the heat to medium-low and add the mozzarella. Stir continuously as the cheese melts. The mixture will initially look stringy, then come together into a smooth, stretchy dough.
Stir in the rose water and remove from the heat.
Roll out the dough.
Let the dough cool just until comfortable to handle, about 5–10 minutes. Divide into 2 portions, keeping the second covered while you work.
Lightly brush two sheets of parchment paper with cooled syrup. Place one dough portion between them and gently roll into a sheet about 1/8 inch thick.
Peel away the top parchment and trim the dough into long rectangles.
Fill and shape.
Pipe or spoon a line of chilled ashta along one long edge of each rectangle, leaving a little space at the ends.
Using the parchment to help lift the dough, gently roll it around the filling into a snug log. Place seam-side down and cut into bite-sized pieces.
Repeat with the remaining dough and filling.
Chill and serve.
Arrange the rolls on a serving plate, cover, and refrigerate until ready to serve.
Garnish with crushed pistachios and optional maraschino cherries. Drizzle with cooled syrup just before serving, or offer the syrup on the side.