1/2 cup butter
1 cup white sugar
1 egg, beaten
1/3 cup all-purpose flour
2 1/2 cups chopped almonds
1 teaspoon vanilla extract
4 cups all-purpose flour
2 teaspoons baking soda
2 teaspoons baking powder
1 teaspoon salt
1 teaspoon almond extract
Melt the butter in a medium saucepan over medium heat. Stir in sugar, beat egg and flour. Beat in nuts, vanilla extract and flour mixture until well blended. Mix in the almond flour mixture. Strain mixture into a medium bowl.
Divide the dough into 8 pieces and roll into balls. Place onto a greased cookie sheet. Brush tops with egg and flour mixture. Brush bottom with almond flour mixture. Seal both edges with butter knife or fork.
Heat the olive oil in a large heavy skillet over medium heat. When olive oil is hot, roll large logs of dough into 1 inch balls. Cook in hot oil until brown on both sides, about 2 inches. Remove to a cooling rack and cool completely.
Lightly butter cookie sheets. Place almonds on cookie sheets. Cover cookie sheets with parchment paper. Roll each log inside the parchment. Place rolled cookie on the parchment. Brush tops with egg and flour mixture and evenly coat the cookie with the melted oil. Remove cookie from parchment and place on baking sheet. Repeat with remaining cookies. Place remaining rolls of dough on top of rolled cookies.
Bake in preheated oven until golden brown, crumbs deflected. Cool cookies on a wire rack for 10 minutes, or until brown. Remove from cookie sheets to wire rack to cool completely. Cool completely on waxed paper, leaving any remaining dough on the sheets.