Preheat oven to 400°F (200°C).

Grease baking pans.

In a large bowl, place 1 cup of flour.

Cut 1/2 cup of cold butter into the flour until the mixture resembles coarse crumbs.

Sprinkle with 2 tablespoons of water and toss with a fork until the mixture forms a ball.

Divide the dough into thirds.

On a floured surface, roll each portion into a 9-in. x 6-in. rectangle.

Place each rectangle on greased baking pans and set aside.

In a saucepan, bring salt and remaining butter (1/2 cup) and water (1 cup) to a boil.

Add the remaining flour (1 cup) all at once and stir until a smooth ball forms.

Remove from the heat and let stand for 5 minutes.

Add the eggs, one at a time, beating well after each addition.

Continue beating until the mixture is smooth and shiny.

Spread the egg mixture evenly over the dough rectangles.

Bake at 400°F (200°C) for 30 minutes, or until puffed and golden brown.

Cool for 10 minutes before removing from pans to wire racks.

For the icing, combine the softened butter, confectioners' sugar, and vanilla extract in a bowl.

Add enough water to achieve the desired consistency.

Spread the icing over the warm coffee cakes.

Sprinkle with chopped walnuts.

Store the coffee cakes in the refrigerator.