Combine 2¾ cups of the flour together with the yeast, sugar and salt in a medium bowl. Whisk together and set aside.

Add the milk to the bowl of a stand mixer fitted with the dough hook. Add the dry ingredients and knead on low speed until a ball of dough forms, about 5 minutes.

Cut the butter into small pieces and add them to the dough. Continue to knead until the butter is fully incorporated and the dough is smooth. The dough should form a ball and begin to clear the sides of the bowl, about 5-6 minutes more. The dough should be sticky but if the dough sticks more to the bowl than itself, add the remaining ¼ cup of flour a small bit at a time as needed.

Wrap the dough in plastic wrap and refrigerate for 1 hour.
To make the butter square:

Using butter that is cold, but not rock hard will make forming the butter square easier. Leave it out at room temp for 15-20 minutes to soften it just a little. (It shouldn't be room temperature)

Toss together the butter pieces and flour on a clean work surface. Smear the butter chunks back and forth using a bench scraper against the work surface until they have combined into a smooth, homogenous mixture. This will take some elbow grease, as you really need to make sure the square is smooth and pliable. **

Wrap the butter mixture in plastic wrap and use the edges of the plastic to form it into a 7-inch square. Refrigerate until ready to use, at least 30 minutes.

Dust a work surface with flour.

Roll the dough into an 11-inch square .

Place the chilled butter square diagonally onto the dough.

Fold the corners of the dough up over the butter square so that they meet in the middle and pinch the edges of the dough together to seal them.

Using a rolling pin, gently tap the dough starting from the center of the dough and working outward, until the square becomes larger and the butter begins to soften. Your goal is to push the butter out the the edges in an even way. (though from my experience even though the butter broke up a bit it still worked just fine.)

Start gently rolling the dough into a 14-inch square, being careful to make sure the work surface stays well-floured and the dough is not sticking.

Fold the dough into thirds to form a long rectangle.

Starting from the narrow ends, fold the rectangle into thirds again to form a square. (This completes two turns of the dough.) Wrap in plastic wrap and refrigerate for 2 hours.

After the dough has chilled, Repeat the folding process, tap the folded dough square starting from the center of the dough and working outward, then rolling out to a 14-inch square. Fold the dough into thirds to form a rectangle and into thirds again to form a square, completing two more turns. Wrap tightly and refrigerate for another 2 more hours.

To shape the croissants, line two baking sheets with silicone baking mats or parchment paper.

Place the chilled dough onto the floured work surface and gently roll into a 20-inch square. (My pastry slab didn't fit this so I did half at a time.)

Cut each half into three rectangles and then slice each rectangle diagonally to yield 12 triangles.

Working with one triangle at a time, gently stretch the dough so that the two long sides are equal in length.

Cut a 1-inch slit in the base of the triangle.

Fold the two corners of the slit outward and begin rolling the triangle up, gently stretching the dough as you roll. Leave the last ¼-inch of the tip unrolled.

Transfer to the prepared baking sheet and fold the ends toward each other to make a crescent shape. Repeat with the remaining portions of dough.

Cover loosely with plastic wrap. Let rise at room temperature until puffy, about 45-60 minutes- they won't double in size, but they will puff up- especially on the edges.

Preheat the oven to 400 F. Brush the shaped croissants lightly with the egg wash- sprinkle with sea salt if desired.

Bake until the croissants are golden brown, 18-22 minutes, rotating halfway through baking. Allow to cool on a wire rack at least 15 minutes. Store airtight at room temperature for up to 2 days.

notes

* Butter should be cold but not too cold- let it sit out at room temperature for 15-20 minutes to soften just a bit
** If you don't have a bench scraper, put the butter between two sheets of plastic wrap, and pound it with a rolling pin.
You may also freeze half of the unbaked croissants for up to two weeks. Simply freeze before proofing, and when you're ready to bake, allow them to come to room temperature and proof as normal. (though they may need a few more minutes.)