Make the thin noodles:
- In a food processor, mix flour and olive oil. Add 1 tablespoon water. Slowly add in eggs, pulsing if necessary to incorporate into dough. If dough appears too dry, add more water, 1 tablespoon at a time.
- Remove dough from food bowl and knead for 5 to 10 minutes. Wrap in plastic and let rest at least 30 minutes. Using a pasta machine, roll to a thin spaghetti shape.
Prepare the pasta:
- Bring a pot of salted water to a boil. In a mixing bowl, combine egg, lemon juice, and Colatura di Alici.
- Cook pasta until just undercooked, then transfer to a medium pan with a couple of spoonfuls of the pasta water. Add butter and swirl to emulsify. Add crab to pan and allow to warm through.
- Pour pasta with crab and butter sauce directly into bowl with egg mixture. Stir to incorporate, adding mustard greens, black pepper, and Piave Vecchio. Season with salt to taste.