Preheat the oven to 300º and place the racks in the upper 2/3 and lower 1/3 of the oven. Line 2 cookie sheets with baking parchment or waxed paper; brush with vegetable oil. Place the almonds in a food processor with the potato starch and pulse finely grind; take care not to over process. Place in a bowl with the sugar.
In a clean bowl, beat the egg whites until stiff but not dry and add the almond extract. Stir in one-fourth into the batter, then fold in the remaining whites until there are no white streaks. Place the mixture into a pastry bag fitted with a 7B or 8 star tip and and pipe out individual cookies onto the prepared pans. Alternately, form mounds with 2 teaspoons.
Place a slivered almond into the center of each.
Bake for 30 to 40 minutes, until the tops are lightly browned. Halfway through baking, switch the positions of the pans fro top to bottom and turn around back to front as well for even baking. Cool on the pans on racks.
Store in airtight containers up to 5 days or freeze up to 2 months.
Makes about 40 cookies.