Preheat oven to 325°F.
Trace the bottom of a 9-10 inch springform pan on parchment paper and cut it out. Attach the pan sides to the bottom. Grease the pan bottom and sides and press the parchment into the bottom. Grease the top of the parchment circle and set aside.
Make the Nut Filling:
Place the pistachios, walnuts, and cardamom into the bowl of a food processor fitted with a metal blade. Pulse to chop into small pieces, mostly 1/4 inch, but some can be larger. You can also chop by hand. Remove to a bowl and set aside. Separate out 3 tablespoons of the nut filling and place in a small cup or bowl to use to sprinkle on top of the cheesecake after baking.
Make the Cheese Filling:
In a blender, place the cream cheese, greek yogurt, and eggs and mix well. Add in the 3/4 cup sugar, honey, and orange blossom water and blend until smooth. Refrigerate until ready to use.
Prepare the Crust:
Melt 6 tablespoons butter in a microwave-safe bowl for 30 to 45 seconds or until melted.
Unwrap the filo dough. Have a damp dishtowel ready to cover the filo as you assemble the cheesecake.
Place one sheet of filo into the springform pan, placing the center in the middle of the pan bottom, against and pressing against the right and left sides of the pan.
Brush melted butter all around the filo. Repeat with three more sheets of filo, moving in a circle to cover all of the interior sides of the pan, brushing melted butter after inserting each filo sheet. Remember to cover the stack of filo with the damp towel when you are not removing sheets to use. Repeat with a second layer of four sheets, again going around in a circle and bushing each layer.
Sprinkle half of the remaining nut filling onto the filo in the pan and spread to cover. Cut two sheets of filo in half. Lay one half sheet on top of the nut filling and brush with melted butter. Repeat with another three half sheets of filo, trying to cover more of the nut filling each time. Sprinkle the remaining nut filling on top. Place a full sheet of filo on top of the nut filling, and brush with melted butter, repeat with three more sheets, moving in a circle. Trim the edges of the filo so there is no overhang.
Assemble and Bake:
Place the springform pan on a baking sheet and pour the prepared cheese filling into the pan. Place in the oven for 45 minutes. About 3 to 5 minutes before the 45 minutes is up, melt the remaining 4 tablespoons of butter.
Cut half of the remaining filo into long 1/4 inch ribbons. Place into a bowl and separate the ribbons. Mix one tablespoon of melted butter into the filo ribbons, and toss gently. Add more ribbons, and more butter, a little at a time until ribbons are just lightly coated with the butter. Do not worry that not all of then ribbons have butter; if you soak the ribbons then they clump up.
After 45 minutes in the oven, remove the cheesecake and carefully sprinkle the filo ribbons on top. Place back into the oven for another 25 minutes. Turn the oven off and use a wooden spoon to hold the door open. Take the cheesecake out of the oven after 15 minutes.
Make the Syrup:
Place sugar, water, and honey into a small saucepan, bring to a boil over high heat. Reduce heat to medium and cook for three minutes or until slightly thickened. Remove from heat and stir in the orange blossom water. Let cool. This can be made 5 days in advance.
When the cheesecake has cooled, pour a little syrup on the top of the ribbons and sprinkle with 1/4 of the remaining nuts. Refrigerate for 6 hours or overnight. To serve, sprinkle with remaining nut filling and syrup over individual slices.
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