For A ingredients: In a medium bowl, cut the butter into the flour until mixture resembles coarse crumbs. Add the cold water one tablespoon at a time. Using your hands or a fork, stir until the dough can form a ball. Divide dough in half. Roll or press each half into a 30.5x8cm inch rectangle. Place them 8cm apart onto an unprepared cookie sheet.
Preheat oven to 200 degrees C.
For B ingredients: In a saucepan, bring the butter and water to a rolling boil. Lower heat and stir in the flour immediately with a wooden spoon. Continue to stir vigorously until the dough forms a tight ball. Remove from heat. Stir in eggs one at a time, then stir in the almond extract. Spread equally onto both rectangles. Bake for 10 minutes before lowering the oven temperature to 165 degrees C. Continue to cook for 15 to 20 more minutes. The top should be crispy and brown.
For C ingredients: To make the glaze, beat the confectioners' sugar together with the melted butter and vanilla until smooth. Spread over the almond puff when cool, and sprinkle with sliced almonds. Cut into strips and serve.