How to Make It
In the bowl of a food processor, pulse both flours with the baking powder, sugar, salt and 1/4 teaspoon of pepper. Add the cubed butter and the oil and pulse until the mixture resembles coarse meal. Add the water and pulse just until the dough comes together. Transfer to a lightly floured work surface and knead several times. Divide the dough in half and form into two 1-inch-thick squares. Wrap in plastic and refrigerate for 1 hour.
Line 2 baking sheets with parchment paper. On a lightly floured work surface, using a lightly floured rolling pin, roll out 1 piece of dough to an 1/8-inch-thick square. Using a fluted pastry cutter, cut the dough into twenty-four 2½-inch squares. Arrange the crackers on the prepared baking sheets, spaced 1/2 inch apart. Poke 4 rows of holes in the center of each cracker. Freeze the crackers until firm, 30 minutes.
Preheat the oven to 400°. Brush the crackers with half of the melted butter; sprinkle with pepper. Bake for 12 to 15 minutes, shifting the pans halfway through. Transfer the crackers to a rack to cool. Repeat Steps 2 and 3 with the remaining dough.
In a food processor, pulse the garlic until finely chopped. Add the remaining ingredients and pulse until well blended. Scrape the pimento cheese into a large bowl and refrigerate for at least 1 hour before serving with the crackers.