In a small bowl, combine the oats and milk and let stand until the oats soften slightly, about 5 minutes.

In a food processor, combine the flour, baking powder, salt, and cayenne pepper (optional) and pulse a few times to blend. Add the cheese and butter and pulse until a coarse meal forms. Stir the beaten egg into the softened oats, then scrape the oats into the food processor. Pulse until a dough forms. Scrape the dough onto a board and gently knead a few times until thoroughly blended. Place the dough into a one-gallon Ziploc bag. Flatten into an even thickness, about 1/8-inch, spreading the dough to the very edges and corners of the bag. Chill flat, at least 1 hour.

Preheat the oven to 375°. Line 2 baking sheets with parchment paper.

Gently split open the Ziploc bag along the side seams. Quickly cut the dough into 1 1/2-inch squares. Brush off any excess flour and transfer the squares to one of the baking sheets. Refrigerate for at least 5 minutes, until the squares are firm.

Combine the beaten egg and milk to make an egg wash.

Lightly brush the squares with the egg wash and lightly sprinkle with sea salt. Bake for about 16 minutes, until the crackers are golden brown. Transfer to a rack and let cool before serving or packaging.