Prepare the dough base: In a large bowl, combine coarse semolina, fine semolina, salt, sugar, and mahlab. Mix well.
Incorporate butter: Add softened butter to the semolina mixture and rub with your hands for about 2 minutes until well combined.
Add yeast and milk: Mix in the instant yeast, then add warm milk gradually while kneading gently for about 5 minutes until a soft dough forms. Cover and let rest for 1 hour at room temperature to ferment.
Prepare the date filling: In a large bowl, combine ground dates, cinnamon, nutmeg, melted butter, and vegetable oil. Mix thoroughly by hand until the mixture is soft and well combined.
Shape the date layer: Form the date mixture into a ball and place it on a piece of plastic in a 12-inch (30 cm) round baking pan. Using your hands, stretch and spread the dates evenly to cover the entire bottom of the pan with uniform thickness. Set aside.
Add orange blossom water and knead dough: Add orange blossom water to the rested dough and knead for another 5 minutes. Divide the dough into two equal parts.
Roll out first dough layer: Place a piece of plastic on the baking pan and spread half of the dough evenly to cover the pan bottom. Remove this dough layer carefully and refrigerate it.
Assemble the maamoul layers: Spread the second half of the dough evenly on the bottom of the ungreased pan. Invert the date layer onto this dough. Then cover the dates with the first dough layer taken from the refrigerator. Smooth the surface and edges to ensure even thickness.
Score and cut: Using a fork, make vertical marks across the surface of the dough. Then lightly score the surface with a knife to create small squares without cutting all the way through.
Bake: Bake in a preheated oven at 400°F (200°C) on the middle rack for about 30 minutes or until golden brown and dark golden color appears. Oven times may vary.
Cool and serve: Remove from oven and let cool completely in the pan for at least one hour before cutting fully along the scored lines and serving.