In a bowl or medium measuring cup, combine the water and yeast. Let it sit in a warm place for 10-15 minutes or until the yeast dissolves.
In the bowl of a stand mixer, combine the flour, sugar, and salt. Then pour in the warm yeast water.
Using the hook attachment, mix the dough on medium speed until it begins to take shape. Toss in 1/2 cup of softened butter and continue mixing on medium high speed until the dough is smooth and well rounded.
Transfer the dough into a bowl greased with oil. Lightly grease the dough with oil as well. Cover with plastic wrap and let it rise for 2 hours or until it triples in size.
Meanwhile prepare the butter slab. Start by cutting out 2 large sheets of parchment paper. Trace an 8x12 inch rectangle on each sheet. Place 1 1/2 cups (3 sticks) sliced butter in the middle of one sheet. Have the traced side down (you don't want to get any pencil marks on the butter).
Place the second sheet on top (traced side up). Using a rolling pin, roll out the butter to the edges of the traced rectangle. Then place on a flat surface in the refrigerator.
Once the dough is done rising, deflate it onto a floured surface and roll it out to a 28x14 inch rectangle. Fold over 2/3 of the left corner then bring in the right corner so it covers the other edge but doesn't quite reach the other side.
Starting from the shorter edge fold the dough into thirds. Cover with plastic wrap and refrigerate for 6-8 hours (or overnight).
In a bowl, combine 1 egg, 3/4 cup butter, and 1/2 tsp almond extract. Then blend in the 2 1/2 cups almond flour, 1 1/2 cups powdered sugar, and 1 tsp corn starch. This will be the almond paste.
Gently deflate the dough onto a floured surface and roll it out to a 25 x 9 inch rectangle. Place the chilled butter slab on the right half of the dough leaving at least 1 inch margin around the edges.
Fold over the left (unbuttered) half and roll the dough out to a 30x12 inch rectangle. It helps to spread the butter by pressing down with the rolling pin along with rolling it out.
Fold over 2/3 of the left corner then bring in the right corner so both edges touch.
Roll the dough out to a 30x12 inch rectangle. Fold it in half like a book. Once its folded in half the dimensions should be 15 x 12 inches. Roll it out to 30 x 12 again.
Then fold it into thirds. If the butter begins to melt, cover with plastic wrap and refrigerate for 30 minutes. The size of the dough should be 12 x 8 inches before wrapping it in plastic wrap.
Cut the chilled dough in half. Rewrap 1 halve and place it back in the refrigerator for later use. Roll the unwrapped dough into a 30x10 inch rectangle and cut out 9 triangles. Each triangle should be about 5 inches at the wide end, and about 1 inch at the narrow end.
I like to make small slit in the middle of the wider ends so the croissant folds nicer, but thats totally optional. Fill the wider end of the triangles with 1 heaping tablespoon of the almond paste. Then roll the triangles toward the narrow end as you slightly pull the pointed end away.
Place the croissants onto a baking sheet lined with parchment paper and let them rise in room temperature for 1-2 hours or until they double in size. Do not put them in a warm place to speed up the rising process. You don't want the butter to melt.
Brush each croissant with egg wash and bake at 390 degrees Fahrenheit for 10 minutes, then 370 degrees Fahrenheit for 15 minutes. Baking time may vary depending on your oven.
Mix the left over almond paste with a splash of milk and spread it over each croissant. Sprinkle sliced almonds over each croissant and bake for another 5 minutes at 370 degrees Fahrenheit. Once their cooled, dust powdered sugar over the top of each croissant.
Remove the second half of the dough from the refrigerator and roll it out to a 30x10 inch rectangle. Cut out 9 triangles and repeat steps 14-17.