Preheat the oven at 425˚F. Line a baking tray with parchment paper. Now take the round base of the baking springform tray ( or a plate of the same diameter) and place it in the center of the parchment paper. Draw the outline circle with a pencil. Set aside.
Meanwhile, pour 1 cup of the water into a saucepan and add 8 tbsp unsalted butter, 1 tsp of sugar, 1/4 tsp salt, 1 tsp of vanilla extract. Set on the stove at low heat. Stir constantly until the butter just melted. When you see the butter melted, stir in 1 cup flour all at once and mix vigorously with a wooden spoon. Cook for about 2-3 mins until the mixture comes together into a smooth ball and doesn’t stick anymore to the sides of the saucepan.
Take the saucepan off the heat and transfer the dough to a stand mixer bowl fitted with the flat beater. Let the dough cool for 4-5 minutes then switch on the mixer on low speed. In 2-3 minutes gradually incorporate 4 eggs - one egg at a time, allowing each egg to fully incorporate between additions. Beat until dough is smooth, shiny, and it falls nicely when you lift it up with a scraper.
Transfer the dough to a pastry bag fitted with a 1/2” round tip. Then take the previously prepared baking tray and pipe two circles of pastry next to each other following the drawn line. Then pipe another one on top of the first two.
Brush the pastry with beaten egg yolk and sprinkle some almond flakes over the top.
Bake the Choux pastry dough at 425˚F for 10 minutes. Then, without opening the oven lower the temperature to 325˚F and, bake for 30 minutes more, until golden brown.
Remove the pastry ring from the oven and transfer to a wire rack to cool completely.