In a large bowl, use an electric mixer to cream together butter, vanilla, almond flavoring, and sugar.
In a separate bowl, sift together flour, baking soda, and salt. Add flour mixture to the butter mixture and mix to combine. It will look crumbly at first, but keep mixing until it comes together in a thick dough. Mix in walnuts.
Shape dough into balls (about the size of golf balls). Place about 1 inch apart on parchment or silicone-lined baking sheets.
Bake for 10-12 minutes or just until set and firm to the touch (but not browned). Allow the cookies to cool for a few minutes, then roll the warm cookies in powdered sugar. Transfer to wire racks to cool completely. Once cool, roll the cookies in powdered sugar again.
The cookies will stay fresh in an airtight container at room temperature for 3-4 days or in the refrigerator for at least 1 week. They do not need to be refrigerated; however, I find that if the house is really humid, the powdered sugar stays dry best when stored in the refrigerator.These cookies freeze really well, too! Just package in airtight containers and store in the freezer for up to 3 months. When thawed, you will probably need to re-roll the balls in powdered sugar.