In a large bowl, use an electric mixture to beat the butter, sugar, salt and vanilla extract until pale and smooth, about 3-4 minutes. Mix in the flour on low speed. Divide the dough in half and form each into a 1-1/2-inch-diamter log. Wrap them with plastic wrap and refrigerate until firm, 1-2 hours.

Preheat the oven to 350 degrees F. Line 2 sheet pans with parchment paper.

In a small bowl, whisk together the egg white and water. Slice the dough 3/8-inch-thick. Brush the edges of each slice with egg wash and roll in the sprinkles. Place the cookies 2 inches apart on the prepared sheet pans.

Bake until the cookies are just starting to turn golden, about 15-20 minutes. Cool on the sheet pans for 2 minutes before transferring to a wire rack. Cool completely before storing in an airtight container.