Preheat oven to 350 degrees. Line 2 large cookie sheets with unbleached parchment paper.

In the bowl of an electric mixer fitted with the paddle attachment, beat together the oil and sugar on medium-high speed until light and fluffy, about 2 to 3 minutes. With the motor running, add the eggs, 1 at a time, allowing each to be incorporated before adding the next. Then add the vanilla and mix until just combined.

In another large mixing bowl, whisk together the flour, baking powder, baking soda, and salt. With the motor of the electric mixer running on low, slowly add the dry mixture to the wet mixture one-third at a time, pausing after each addition. Mix just until the dough no longer sticks to the sides of the bowl, being careful not to over-mix, or your cookies will be tough. Remove the bowl from the mixer and work the almonds into the dough by hand.

Very lightly oil a marble baking slab or a large plastic cutting board as well as your hands, and lightly oil a large serving spoon to use as a measure. Scoop out a heaping portion of the dough with the oiled serving spoon and shape into the form of a long pretzel roll or a small baguette, about 9 inches long. Continue with the remaining dough. You should end up with 5 (9 × 3-inch) logs of dough. Keep some paper towels nearby in case your hands or the surface gets too greasy. Transfer the dough logs to the prepared cookie sheets, taking care not to place them too close together, as they will expand in the oven.

Transfer to preheated oven and bake for 20 to 25 minutes, until lightly browned. Remove from oven, cool for a few minutes until cool enough to handle, and, using a serrated knife, cut each log into 3/4-inch slices on a slight diagonal angle. Lay the slices cut side down on the same baking sheets, and return them to the oven to crisp up for another 15 to 20 minutes, or until golden. Paksimathia will keep in an airtight container at room temperature for up to 1 week.