Bring a large pot of salted water to the boil. Add the green beans and boil just until tender, 2 to 3 minutes. Drain the beans, and immediately shock them in a bowl of ice water to stop the cooking.
When the beans are just cool, drain again. Coarsely chop the beans into pieces approximately 1 1/2 inches in length and place in a large bowl.
In a large sauté pan, heat the olive oil over medium high heat until hot. Add the onion and cook, stirring frequently, until the onions are translucent and begin to color, 8 to 10 minutes.
Stir in the chopped garlic and continue to cook until the onion is caramelized, 6 to 8 minutes. Remove the pan from heat and cool slightly, then toss the onions and garlic with the green beans.
Meanwhile, in a medium bowl, whisk together the eggs, Parmigiano-Reggiano, milk, one-fourth teaspoon salt and several grinds of pepper. Stir the egg base in with the beans and onion mixture.
Heat the oven to 350 degrees F. Line a 9-inch springform pan with foil, and grease the foil.
Pour the bean mixture into the pan and sprinkle over the bread crumbs. Bake the tortino until set (it should barely jiggle, and a knife inserted will come out clean), 30 to 40 minutes. Remove and cool the tortino, still in the pan, on a rack.
When the tortino is cool, cover the pan and refrigerate it until chilled (chilling the tortino will make it easier to slice). Serve the sliced tortino cool or at room temperature.