Preheat oven to 325 degrees F. Blend and pulse the 1/2 cup nuts in a food processor with the sugar until mixture resembles coarse sand. (If there are a couple small chunks of nuts that is fine.) Add the butter, vanilla and almond extracts, and the salt, and pulse until creamy. Add the flour and continue to pulse to make a soft dough.
Turn the dough out into a 9-inch tart pan and spread it out evenly with an off-set spatula. Dip the spatula in a little warm water to help smooth and even the surface of the shortbread. Cover and freeze until firm, about 20 minutes.
Put the tart pan on a baking sheet and dock (prick) the dough all over with a fork. Generously sprinkle the top of the shortbread with sugar. Toss the remaining whole almonds in the egg white; evenly arrange and press the nuts into the dough around the edge of the pan. Bake until golden brown and set, about 1 hour and 10 minutes.
Cool the short bread in the pan on a rack for 10 minutes. Carefully remove the tart ring and cut the shortbread with a sharp knife into wedges, each with a nut. Cool shortbreads on a rack completely. (Alternatively present the shortbread as 1 large cookie. Cool the shortbread in the pan completely and remove the tart ring. Cut the shortbread into wedges as desired.) Serve. Store in a tightly sealed container for up to 5 days.