Position two racks in the middle and upper third of the oven. Heat the oven to 350°F. Line two baking sheets with nonstick liners, like Silpat brand, or with parchment.
In a food processor, grind the almonds finely and measure out 1/2 cup. Heat the butter, sugar, and corn syrup in a medium saucepan over low heat, stirring often, until the butter melts and the sugar dissolves. Increase the heat to medium high and, stirring constantly, bring the mixture just to a boil. Remove the pot from the heat and stir in the flour and salt until incorporated. Stir in the remaining ground almonds and the vanilla.
Drop the batter by the teaspoon 3 inches apart on the baking sheets, about six cookies per baking sheet. Bake the cookies until evenly light brown, about 10 minutes total. About 5 minutes into baking, switch the sheets from top to bottom and back to front to promote even baking. The cookies won’t begin to spread until about 6 minutes into baking.
Line a wire rack with paper towels. Remove the cookies from the oven and, as soon as they’re firm (which will take just a few minutes), use a wide spatula to transfer them to the rack to cool completely.
Bake off the remaining cookies; the batter will have firmed up a bit, but that’s fine.
The cookies will stay crisp and flavorful for a few days wrapped in waxed paper or plastic wrap at room temperature. They also freeze well in a tin or sturdy plastic container.