In a large bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add brown sugar, baking soda, and salt. Beat until combined, scraping the sides of the bowl occasionally. Beat in oil, egg, and vanilla. Beat in as much of the flour as you can with the mixer. Stir in any remaining flour and the 3/4 cup almonds. Divide dough in half. Cover and chill dough about 2 hours or until easy to handle.
Preheat oven to 375 degrees F. On a lightly floured surface, roll dough, half at a time, to 1/4-inch thickness (keep remaining dough refrigerated). Using 1 1/2- to 4-inch star-shape cookie cutters, cut dough into star shapes. Place 1 inch apart on an ungreased cookie sheet.
Bake for 6 to 8 minutes or until edges are lightly browned. Transfer to a wire rack; cool.
If desired, in a small saucepan, heat and stir chocolate and shortening over low heat until melted; cool slightly. Decorate cookies with melted chocolate and, if desired, additional almonds. Let stand until chocolate is set.