Preheat your oven to 350°F (177°C).
Make the short crust base: Add 1 cup all-purpose flour to a medium bowl. Cut in 1/2 cup softened butter using a pastry blender or two forks until the mixture resembles coarse crumbs.
Sprinkle 2 tablespoons of room-temperature water over the mixture. Stir with a fork until the dough just comes together. Divide in half and press each half into a 12 x 3 inch rectangle on an ungreased cookie sheet, spacing them about 3 inches apart.
Make the choux topping: Combine 1/2 cup butter and 1 cup water in a medium saucepan over medium heat. Bring to a full rolling boil, then immediately remove from heat.
Stir in 1 tsp almond extract. Add 1 cup flour all at once and stir vigorously. Return to low heat and stir for about 1 minute until the dough pulls away from the sides and forms a ball. Remove from heat and let cool 2–3 minutes.
Add eggs one at a time, beating thoroughly after each addition, until the mixture is smooth and glossy.
Assemble: Divide the choux topping in half and spread evenly over each short crust rectangle, pushing all the way to the edges.
Bake for 55–65 minutes until the top is deep golden-brown and looks dry and crisp. The pastry will puff up dramatically then collapse when removed from the oven — this is completely normal.
Transfer both strips to a wire cooling rack and cool for at least 30–40 minutes before glazing.
Make the glaze: Mix powdered sugar, softened butter, almond extract, and 1 tablespoon warm water or milk until smooth. Adjust consistency as needed. Spread or drizzle over cooled pastry strips.
Immediately scatter toasted sliced almonds over the wet glaze. Let set for 15 minutes, then slice and serve.