1. In medium bowl, stir flour, parsley, lemon peel, baking powder, pepper, and 2 teaspoons salt. Add 3/4 cup water; stir until dough comes together in a ball. With hand, knead dough in bowl until smooth, about 2 minutes. Divide dough in half; cover each half with plastic wrap and let rest 10 minutes.
2. Preheat oven to 350 degrees F. On floured surface, with floured rolling pin, roll half of dough into paper-thin rectangle, about 18" by 12" (don't worry if edges are irregular). With pizza wheel or sharp knife, cut dough lengthwise in half to form two 18" by 6" rectangles. Cut rectangles crosswise into 2-inch-wide strips.
3. Transfer strips to 2 ungreased large cookie sheets (it's alright if dough stretches a little); let rest 10 minutes. With pastry brush, brush strips lightly with 1 tablespoon olive oil; sprinkle with 1/4 teaspoon salt.
4. Place cookie sheets on 2 oven racks. Bake strips 15 to 18 minutes until lightly browned, rotating cookie sheets between upper and lower racks halfway through baking time. Immediately remove crisps to wire racks to cool.
5. Repeat with remaining dough, oil, and salt. Store crisps in tightly covered container to use within 2 weeks.