Activate the Yeast: In a small bowl, combine the warm water and yeast. Let it sit for about 5-10 minutes until it gets foamy.
Make the Dough: In a large bowl, whisk together the sugar, warmed milk, and salt. Add the foamy yeast mixture. Gradually add 3 1/2 cups of flour, mixing until a shaggy dough forms.
Knead the Dough: Turn the dough out onto a lightly floured surface. Knead for about 5-7 minutes, adding a little more flour if needed, until the dough is smooth and elastic.
Incorporate the Butter (First Fold): Roll the dough out into a large rectangle (about 12x18 inches). Place the cold butter pieces evenly over two-thirds of the dough. Fold the unbuttered third over half of the buttered section, then fold the remaining buttered section over that.
First Chill & Turn: Wrap the dough tightly in plastic wrap and chill for at least 30 minutes. After chilling, place the dough on a lightly floured surface with a short side facing you. Roll it out into a large rectangle again, then fold it into thirds like a letter.
Second Chill & Turn: Wrap the dough and chill for another 30 minutes. Repeat the rolling and folding process (another 'turn').
Third Chill & Turn: Wrap the dough and chill for another 30 minutes. Repeat the rolling and folding process (another 'turn').
Final Chill: Wrap the dough tightly and chill for at least 2 hours, or preferably overnight.
Make the Almond Filling: While the dough chills, make the filling. In a medium bowl, combine the almond flour, sugar, softened butter, egg, almond extract, and salt. Beat with an electric mixer until smooth and creamy.
Shape the Croissants: Take the chilled dough out of the refrigerator. On a lightly floured surface, roll it out into a large rectangle (about 1/4 inch thick). Cut the dough into long triangles.
Fill & Roll: Spread a spoonful of almond filling along the base of each triangle. Starting at the base, roll up each triangle towards the point.
Proof the Croissants: Cover the croissants loosely with plastic wrap and let them rise in a warm place for about 1-2 hours, or until they're puffy and almost doubled in size.
Prepare the Egg Wash: Whisk together the egg and milk in a small bowl.
Bake the Croissants: Preheat your oven to 375°F (190°C). Brush the risen croissants with the egg wash and sprinkle with sliced almonds. Bake for 18-22 minutes, or until they're golden brown and cooked through.
Cool & Dust: Let the croissants cool on the baking sheet for a few minutes before transferring them to a wire rack. Dust generously with powdered sugar before serving.