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In a large bowl, whisk together the flour, sugar, sesame seeds, almond flour, and salt. Work the butter into the flour mixture until the butter is in small chunks.
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With your fingertips, lightly toss and rub the mixture together until it resembles coarse meal.
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Combine the vanilla and water in a small cup. Drizzle the flour mixture with the water and vanilla, tossing it with a fork as you go. The dough should be evenly damp, but remain crumbly and stick together only when pinched.
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Line a 9" x 5" loaf pan with plastic wrap, and pour the mixture into it. Cover with plastic wrap, and press it down very firmly to an even, compact layer about 1/2" thick. Refrigerate for 2 hours or overnight.
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To bake: Preheat the oven to 350°F. Line two baking sheets with parchment.
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Unwrap the dough and place it on a cutting board. Using a long, sharp knife, cut the dough crosswise into 1/4" (or thinner, if possible) slices. Use the knife to transfer each slice to the prepared baking sheets, laying them flat and placing them 1" apart.
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Bake the sticks for 12 to 18 minutes, until they're golden brown. Remove from the oven and cool on the pan before transferring to an airtight container once completely cooled.