Whisk salt, flour, finely ground toasted almonds, cocoa, and powdered sugar in a medium bowl until thoroughly combined.
Using an electric mixer, beat butter in a large bowl until creamy. With mixer running, slowly pour in olive oil; mix well, then gradually add granulated sugar and vanilla extract.
Slowly stir in flour mixture until just blended. Form dough into a large ball, flatten into a disk, wrap in plastic wrap and chill for at least 2 hours or overnight.
Remove the dough and allow to sit at room temperature for 20 minutes.
Preheat the oven to 375.
Press the dough into an ungreased 11" fluted tart pan with removable bottom. Bake for 15-17 minutes until slightly firm to the touch. As soon as the pan is removed, take a very sharp knife and carefully cut the shortbread into wedges, making sure to slice completely though the dough. Allow to cool completely and remove from tart pan.
Dust with additional powdered sugar.