Mix together the water, yeast and 1 tsp sugar. Cover, and set aside in a warm place (like the microwave) to proof.
Meanwhile, in a large bowl, mix the flour, sugar and salt together. Make a well with the dry ingredients and add the yeast mixture. Add the beaten egg and mix with a wooden spoon, switching to your hands with the spoon starts to be more difficult. Wrap the dough in plastic wrap and refrigerate for 30 minutes.
Add the butter to a cutting board. Cover with a piece of parchment or wax paper, and pound flat into a square. Set aside.
Once the 30 minutes is up, roll out the dough on a floured surface until1 cm thick. Place the square of butter on top of the dough, centered, with a border of dough around it. Fold the edges of dough so that the butter is still visible. This should form a square. Then fold the square in half to make a rectangle. Finally, fold the rectangle in half to make a smaller square. Wrap the dough and refrigerate for 30 minutes.
Once the 30 min is up, roll the dough into a 1 cm thick rectangle. Then, just as above, fold the edges of the dough together to form a square. Fold the square in half to form rectangle, and then again to form another square.
Once the 30 minutes is up, roll out the dough until a thickness of 1 cm (in a rectangular shape). With a sharp knife, cut the edges to form a rectangle. Then cut the rectangle horizontally in half. You should now have two rectangular strips. Cut congruent equilateral triangles across the strips (in the shape of Pillsbury crescent rolls- come on, you know it). Pull apart and set aside.
Preheat the oven to 350F. Fill the triangles as desired - they may be easier to pull a little at room temperature.
Bake 12-15 minutes until golden brown. While the croissants bake, make the glaze by adding the sugar and water to a small saucepan. Heat until the sugar dissolves and let simmer about 5 minutes, stirring frequently. Remove from heat and add vanilla.
Once the croissants are out of the oven, brush with glaze and serve immediately.