Stir the flour and baking powder together in a medium-size bowl, and set it aside.
Whisk the eggs, sugar, oil, and vanilla in a large bowl. Gradually stir in the flour mixture, followed by the chocolate chips. The dough will be very sticky. Cover the bowl and refrigerate overnight.
Preheat the oven to 350°F and line a baking sheet with parchment paper.
Divide the dough into 2 rectangular logs. Place the logs on the prepared baking sheets and bake them until the tops are firm to the touch, about 25 minutes.
Remove the baking sheets from the oven, but leave the oven on. Let the logs cool for 5 minutes on the baking sheets, then, using a serrated knife, cut each log diagonally into 3/4-inch-thick slices.
Place the slices, cut side down, back on the baking sheets, and bake for 7 more minutes.
Turn the oven off and leave the cookies in the oven for at least 1 hour, so they will dry completely.
Because most of the moisture is baked out of them, these cookies have a fairly long shelf life: store them in an airtight container or in a tin box, and they will keep virtually forever.