On a clean work surface or in a large bowl, combine both flours. Make a well in center; add eggs and yolks, 1 tablespoon warm water, and oil. Using a fork and whisking outward from the center of well, gradually incorporate flour mixture into egg mixture until a ragged dough forms.
Transfer to a lightly floured work surface and knead until dough is smooth and springs back when pressed with a finger, 8 to 10 minutes. While kneading, add more water, 1 tablespoon at a time, if dough feels too dry; or add more "00" flour, 1 tablespoon at a time, if dough feels too sticky.
Divide dough in half. Pat each half into an approximately 1-inch-thick square; tightly wrap in plastic and let stand at least 1 hour and up to 3 hours before using.