Boil the green beans until just slightly underdone and drain them well.
While the green beans are boiling, sweat some chopped onion in olive oil in a heavy pot or casserole and, when the beans are done, drain them and add them to the oil and onions. Mix well to coat the beans and cover the pot. Allow the beans to braise, turning them from time to time, until they are quite tender.
Just before serving, while the beans are still quite hot, take the pot off the heat and immediately add a mixture of egg yolk and lemon juice, seasoned with salt and pepper. Mix well, allowing the mixture to thicken using just the residual heat in the pot, until a creamy 'sauce' coats the beans well.
Serve your fagiolini in fricassea immediately.