Cut 1 pound each carrots and parsnips into fries (cut around the parsnips' cores); toss with 1 tablespoon vegetable oil and 1 teaspoon each lemon-pepper seasoning and kosher salt. Toss with 2 beaten egg whites, then coat in 1/2 cup panko breadcrumbs. Spread out on 2 baking sheets. Bake at 400 degrees F, stirring once, until crisp, about 35 minutes.