In a medium bowl, combine flour, salt, and baking powder. Set aside. In a large bowl, use a hand beater or whisk vigorously to mix olive oil and sugar, then the eggs. Add dry ingredients to liquids and stir until it comes together in a dough. Stir in almonds. Divide dough in half and wrap each half in plastic wrap. Chill for one hour or more.
Adjust oven rack to middle position and preheat oven to 350°F. Line two baking sheets with parchment paper.
Form each half of dough into a log that is approximately 3 ½-inches by 8-inches. Place one on each baking sheet. Bake until golden, about 45 minutes. Take loaves out of the oven. Decrease oven temperature to 300°F.
When cool enough to handle, use a serrated knife to cut logs on the bias to form 1-inch wide cookies (or whatever shape you like). Place cookies, cut side down, on baking sheet. Bake until dry and toasted, about 5-6 minutes.
Put icing sugar in a small mixing bowl. Add vinegar and mix vigorously with a spoon. Add water by ½ teaspoons until the icing is a consistency appropriate for drizzling.