Step 1

In a large bowl, whisk together both flours, the salt, baking powder, paprika and pepper. Add the sesame, fennel and poppy seeds; toss well. Add both oils and ½ cup water. Using a silicone spatula, stir until a shaggy dough forms; it’s fine if some dry pockets remain.

Step 2

Lightly dust the counter with all-purpose flour and turn the mixture out onto it. Knead by hand just until the dough is pliable, evenly moistened and only slightly sticky; it will not form a smooth ball. Do not overknead. Divide the dough in half and shape each portion into a 1-inch-thick disk. Wrap each in plastic and refrigerate for at least 1 hour or up to 24 hours.

Step 3

About 20 minutes before you are ready to bake, remove the dough disks from the refrigerator. Heat the oven to 350°F with racks in the upper- and lower-middle positions. Have ready 2 baking sheets and two 12-by-16-inch sheets of kitchen parchment.

Step 4

Place 1 parchment sheet on the counter and lightly dust with all-purpose flour. Unwrap 1 dough disk and place it on the parchment. Using a lightly floured rolling pin, roll the dough to an even ⅛-inch thickness; it’s fine if the dough is oddly shaped. If the dough tears or resists rolling, it’s too cold; cover and let stand a few minutes before continuing. Transfer the parchment with the rolled dough to a baking sheet. Lightly brush all over with olive oil.

Step 5

Using the second parchment sheet, roll out the remaining dough disk in the same way and brush with olive oil. Use a fork to poke holes every 1 to 2 inches across the surface of the dough sheets, then sprinkle with flaky salt (if using).

Step 6

Bake until the cracker sheets are crisp and beginning to brown, 25 to 35 minutes, rotating the baking sheets and switching their positions about halfway through. Cool completely on the baking sheets on wire racks. Break the cracker sheets into 1½- to 2-inch pieces or shards.