Preheat the oven to 350 degrees F. Butter the bottom and sides of a 9-inch square baking dish. Combine the almond paste, whole eggs, egg yolks, melted butter and 1/4 cup sugar in a food processor. Pulse until combined with a few small lumps of almond paste. Add 1 tablespoon orange blossom water, the baking powder, salt and vanilla; pulse to combine. Add the phyllo pieces and pulse until finely chopped. Spread the mixture evenly in the prepared pan. Bake until golden brown and firm on top, 25 to 30 minutes.
Meanwhile, make the syrup: Heat the orange juice, honey, lemon juice, the remaining 3/4 cup sugar and the remaining 1 tablespoon orange blossom water in a small saucepan over medium heat, stirring, until dissolved, about 5 minutes. Remove from the heat and cover to keep warm.
Remove the baking dish from the oven and immediately pour half of the syrup over the cake; let soak in, 15 minutes. Add the pistachios to the remaining syrup and pour over the cake, spreading the pistachios with a rubber spatula. Transfer to a rack and let cool completely in the pan, about 3 hours, tipping the pan occasionally to distribute the syrup. Cut diagonally into small diamonds.
Photograph by Ryan Dausch