Adjust oven rack to middle position and heat oven to 325 degrees.
Pulse 1 cup almonds in food processor until coarsely chopped; transfer to bowl and set aside. Process remaining 1/4 cup almonds in food processor until finely ground, about 45 seconds. Add flour, baking powder, and salt; process to combine. Transfer flour mixture to second bowl.
Process 2 eggs in now empty food processor until lightened in color and almost doubled in volume, about 3 minutes. With processor running, slowly add sugar until thoroughly combined, about 15 seconds. Add melted butter, almond extract, and vanilla and process until combined, about 10 seconds.
Transfer egg mixture to a bowl large enough to mix all ingredients. Sprinkle half of flour mixture over egg mixture and gently fold until just combined. Add remaining flour mixture and chopped almonds and gently fold until just combined. Divide batter in half.
Using floured hands, form each half into 8 by 3-inch rectangle. Spray each loaf lightly with oil spray.
Bake until loaves are golden and just beginning to crack on top, 25 to 30 minutes, rotating pan halfway through baking. Let loaves cool on baking sheet for 30 minutes. Transfer loaves to cutting board and using serrated knife, slice each loaf on slight bias into 1/2-inch-thick slices.
Lay slices cut side down, on rimmed baking sheet. Bake until crisp and golden brown on both sides, about 35 minutes, flipping slices halfway through baking.
Adapted from America’s Test Kitchen