Mix the yeast with half a cup of warm water, 1 teaspoon of the flour, and 1 teaspoon of the sugar. Stir well. Cover and let the starter rest.

Mix the softened butter with the sugar until well combined. Add the egg and vanilla extract. Mix well, then add the milk. Stir in 3/4 cup of the flour (about 100 grams) to make a creamy dough.

Add the rested starter to the creamy dough. Mix well, then add 2 1/2 cups of flour (about 300 grams). Combine, then transfer the dough to a floured surface. Gradually knead in the remaining 3/4 cup flour (about 100 grams), adding a little more if needed, but not too much or the croissants will be dry. Knead for 5–10 minutes. Place the dough in a bowl, cover, and let rest for 15 minutes.

After 15 minutes, roll out the dough into a rectangle and cut into triangles to shape the croissants. Roll them up and place on a greased baking sheet, parchment paper, or silicone mat.

Brush with beaten egg and bake in a preheated oven at 350°F (180°C) for about 20 minutes. They're ready! They're delicious! You can brush them with syrup on top for an extra special touch.