In a large bowl, use an electric mixer to cream the softened butter with the granulated and brown sugars until light and fluffy.
Beat in the vanilla extract and ground almonds until well blended.
In a separate bowl, whisk together the flour and salt. Gradually add the dry to the butter mixture, mixing on low speed just until combined. Be careful not to overmix the dough.
Transfer the dough to a large sheet of wax or parchment paper. Use your hands to shape the dough into a log approximately 2 inches in diameter.
Roll the log tightly in the paper and refrigerate for at least 1 hour, or up to 1 week.
When you're ready to bake, preheat your oven to 350°F / 175°C. Prepare a cookie sheet by lining it with parchment paper or leaving it ungreased.
Unwrap the chilled dough log and use a sharp knife to cut it into slices ¼-inch thick.
Arrange the slices on the prepared cookie sheet, about 1 inch apart.
Bake for 12 to 15 minutes, or until the edges are lightly golden. These cookies will not spread much during baking.
Let them cool on the cookie sheet for a few minutes before transferring to a wire rack to cool completely. Store in an airtight container for up to 2 weeks.
Do not overmix the dough after adding the flour.
Mixing just until combined is the key to a tender, crumbly cookie rather than a tough one.