Pre-heat oven to 350 - toast halved almonds for 8-11 minutes or until golden brown all the way through the middle (will be fragrant). Leave oven pre-heated at 350 for biscotti.
Using stand or hand-mixer with whip attachment on med-high speed beat together eggs, sugar, and vanilla for 5-6 minutes or until thick and lemon colored.
In a large bowl stir together flour, baking powder, salt, and toasted almonds. Pour egg mixture into flour mixture and stir with wooden spoon for approximately 2-3 minutes until thoroughly combined (mixture will be fairly stiff).
Turn dough onto parchment lined baking sheet, forming a log about 5 inches wide and 12 inches long. If you dampen your hands it'll be easier to pat the form into shape without it sticking to your hands.
Bake log(s) for 50-60 minutes on center rack until a bit past golden brown and firm. (Test by pressing a fingertip it should not yield to pressure). Cool on a rack about 15 minutes, then at a diagonal slice into 1-inch wide biscotti.
(At this point it can be frozen for up to a month prior to baking and can be baked directly from freezer)
Return biscotti cut side down to the oven for 3-4 hours or until completely baked through. To test for doneness, poke-- it should be rock hard. Let cool. Can be stored in airtight container for up to 2 weeks.