Preheat the oven to 350°F (175°C). Grease a baking dish with the ½ tbsp olive oil or butter.
If not already done, trim the tips from the green beans. Place the beans in a large saucepan, cover with water, add salt (to taste), bring to a boil, and cook about 10 minutes until the beans are tender but still bright green.
While the beans cook, make the breadcrumb topping: place the day-old bread cubes, Parmesan shavings, walnuts or pecans, chopped garlic cloves, and the ¼ cup olive oil or butter in a food processor. Pulse 5–10 seconds (or until the mixture forms coarse breadcrumbs).
Drain the cooked beans well and gently toss them with a little olive oil or butter and additional salt if desired.
Transfer the drained beans to the greased baking dish in an even layer. Evenly spread the breadcrumb mixture over the beans.
Bake in the preheated oven 15–20 minutes, until the breadcrumbs are golden brown.
Remove from the oven, sprinkle lemon juice to taste over the dish, and serve.