Step 1In a prepared steamer, or in a steamer unit set over a pot of boiling water, steam the green beans until they are crisp but tender, about 5 minutes. Remove from heat and shock the green beans in a bowl of ice water to stop the cooking. Drain well, then coarsely chop and set aside in a large bowl.
Step 2In a large frying pan, heat the oil over medium heat. Add the onions and reduce heat slightly, sauteing the onion until deeply golden, about 30 minutes, stirring frequently. Remove from heat and add the onions and oil to the bowl with the beans.
Step 3To the bowl, add the eggs and walnuts. Season the mixture with 1 1/2 teaspoons salt, one-fourth teaspoon white pepper and several grinds of black pepper. Move the mixture to a food processor or grinder and process until finely ground (this will probably need to be done in two batches). Taste and season again if desired, then cover the mixture and refrigerate it to give it a chance to firm up, at least 1 hour.
Step 4To serve, make a bed of lettuce leaves on each serving plate and top with a small ball of the mixture (use a lightly oiled ice cream scoop if you have one). Garnish each serving with a radish slice or cherry tomato. Serve immediately.