Using a stand mixer with a dough hook attached, add the flours and salt to the bowl. Mix on low to combine. Slowly add the water and the olive oil while the mixer is running and knead until a smooth dough forms, 7 to 9 minutes. Turn the dough onto a lightly floured surface and knead by hand to form a smooth ball. Cut the ball into 4 even pieces, brush each ball with olive oil, and cover with plastic wrap. Let the dough rest for 1 hour.

Adjust the oven racks to the upper-middle position and the lower-middle position and heat the oven to 425 degrees. Lightly coat two large (about 18 by 13 inches) rimless baking sheets (or invert one) with cooking spray.

Working with two pieces of dough (keep the other two covered), shape one piece of dough into a rectangle and then put it on the baking sheet. Use a rolling pin and your hands to roll and stretch the dough evenly to the edge of the baking sheet. Use a fork to poke holes in the dough ever 2 inches. Brush the dough with a beaten egg and then sprinkle each piece of dough with 1 1/2 teaspoons sesame seeds, 1/2 teaspoon salt, and 1/4 teaspoon pepper. Gently press the seasonings into the dough with your hands to help them adhere. Repeat with second piece of dough on a second baking sheet.

Bake crackers until deeply golden brown, 15 to 18 minutes, switching and rotating the sheets halfway though baking. Transfer the crackers to wire rack to let cool. Let the baking sheets cool completely and repeat with remaining dough. Break cooled lavash into large crackers and serve. Crackers can be stored at room temperature for up to 2 weeks.