Pulse the sugar and salt in a food processor until the sugar is fine and powdery. Add the almonds and pulse until they are finely ground. Add the butter in large chunks, along with the vanilla and almond extracts. Pulse until the butter is smooth. Add the flour and pulse until a soft dough begins to form around the blade. Transfer the dough to a large bowl and knead it briefly to make sure it is mixed evenly.

Form a log about 12 inches long and 1-3/4 inches in diameter. Wrap the log in wax paper or foil. Refrigerate at least 2 hours and preferably overnight.

Preheat the oven to 350 degrees F. Position a rack in the center of the oven.

Spread the coarse sugar on a sheet of wax paper or a flat dish. Roll the dough log in the sugar, pressing so that the sugar adheres. Cut the log into slices 1/4-inch thick and place them at least 1 inch apart on the ungreased or lined cookie sheets. Bake for 12 to 15 minutes, until the edges are golden brown, rotating the pan from front to back halfway through the baking time to ensure even baking. For lined pans, set the pans or just the liners on racks to cool. For unlined pans, let the cookies set on the pan for a minute or two before transferring them to a rack with a metal spatula. Cool the cookies completely before storing. May be kept in an airtight container for up to 1 month.