In a large mixing bowl, combine all of the flours together.
Cut cold butter into the flour blend using your hands or a pastry cutter until the mixture is crumbly.
Sprinkle with water and gently bring the dough together just until it forms a rough ball.
Press the dough evenly into the bottom of a greased 8x8-inch baking pan and set aside.
In a medium saucepan, bring butter and water to a rolling boil.
Remove from heat and quickly stir in the almond extract and flour.
Return to low heat and stir vigorously with a wooden or silicone spoon until the mixture forms a smooth ball, about one minute.
Remove from heat again and let cool slightly.
Beat in the eggs one at a time, mixing well after each addition until the batter is smooth and spreadable.
Spread the egg layer evenly over the prepared base layer.
Bake at 350°F for 50–60 minutes, or until the top is puffed, golden brown, and crisp.
Allow the pastry to cool completely in the pan.
In a small bowl, whisk together powdered sugar, almond extract, and enough milk to create a thick glaze.
Drizzle glaze over the cooled pastry and top with slivered almonds, if desired.