Make the filling: Heat oven to 350°. Place almonds on a rimmed baking sheet, and place in oven; bake, stirring once, until lightly toasted, about 8 minutes. Transfer to a wire rack, and let cool. Transfer almonds to a food processor, and add sugar; process until very finely ground. Add vanilla, salt, cinnamon, egg white, and 2 tbsp. water, and process until a moist, slightly sticky paste forms. Transfer to a bowl, and set aside.
Form the pastries: Place 2 sheets of phyllo dough on a work surface and cut lengthwise into 4 equal strips. Place 1 tbsp. filling at the end of each strip closest to you. Working with one strip at a time, fold the right corner over filling so that it lines up with the left side, forming a triangle; continue folding triangle along the strip as you would fold a flag, until it reaches the end. Brush the end portion of each strip with water, and then fold over pastry to seal; repeat folding with remaining strips, and then repeat filling and folding process with remaining phyllo sheets and filling.
Pour oil to a depth of 2" in a 6-qt. Dutch oven, and heat over medium-high heat until a deep-fry thermometer reads 350°. Working in batches, add pastries to oil and fry, tossing occasionally, until golden brown and filling is hot, about 1-2 minutes. Using tongs, transfer pastries to a wire rack set over paper towels to drain; set aside.
Meanwhile, bring sugar and 1 cup water to a boil in a 2-qt. saucepan over high heat, stirring to dissolve sugar, about 3 minutes. Remove from heat, and stir in honey, juice, and orange flower water. Transfer pastries to a rimmed baking sheet so they sit in one even layer. Pour hot syrup evenly over pastries, and let sit until pastries soak up some of the syrup, about 10 minutes (they will not soak up all the syrup). Let sit 10 minutes before serving.