Pat the chicken dry and season with kosher salt and black pepper on both sides.
In a large pan, heat 2 tablespoons extra virgin olive oil over medium-high heat. Add the chicken and sear until brown on both sides (about 5 minutes or so). Remove the chicken from the pan and set aside for now.
In the same pan, add the onion slices and garlic, if needed, add a little more olive oil. Season with a good pinch of kosher salt. Cook over medium heat, tossing regularly until softened.
Add ¾ cup of water and the spices. Bring to a boil, then return the chicken pack to the pan. Cook over medium-high heat for about 10 to 15 minutes or until the chicken is fully cooked through and the liquid has reduced by ½.
Carefully remove the chicken from the pan onto a cutting board. Using two forks (or a fork and knife), shred or break the chicken up into small pieces.
To the pan of liquid, stir in the beaten eggs. Return the chicken to the pan and stir to combine. Stir in the chopped dates, almonds, and parsley. Remove from the heat
Turn the oven on to 375 degrees F and adjust a rack in the middle.
Prepare a 10-inch pie dish or heat-safe skillet and brush the bottoms and sides with extra virgin olive oil.
Take one sheet of phyllo dough and fold it in half vertically (the long way). Brush the top of the folded phyllo with extra virgin olive oil. Now lay the folded phyllo sheet in the middle with the sides hanging on either side of the pan. Repeat with 7 more sheets of the phyllo, making sure each sheet is folded and brushed with oil. Layer the phyllo sheets in the pan so that they overlap, rotating the pan so that the phyllo will cover it on all sides (there should be phyllo slack hanging over on all sides of the pan).
Spread the chicken mixture over the phyllo. Cover with the remaining 2 sheets of phyllo, making sure to brush each layer with olive oil. Fold the phyllo sides (or slack) over to cove. Brush the top with extra virgin olive oil.
Bake on the center rack of your heated oven for 15 to 20 minutes or until the phyllo is fully cooked and golden brown (rotate the pan occasionally to make sure you get even color on all sides).
Tips for working with phyllo: Thaw phyllo overnight, allow it to come to room temperature before using it, and cover sheets of phyllo with a damp cloth to prevent them from drying out and breaking.
Make-ahead option: You can make the chicken filling a day in advance.
Leftovers and storage: Leftovers will keep for three to four days in an airtight container in the fridge. To reheat, brush the top of the pastilla lightly with extra virgin olive oil again and place it on a sheet pan in a 375 degrees F-heated oven for a few minutes until warmed through.