Break the cornbread into bite-sized pieces and transfer to a rimmed baking sheet. Let dry overnight.
Heat oven to 400 F. Drizzle cornbread with 2 teaspoons olive oil and bake until golden brown and crisp, about 8 minutes. Set aside.
Heat a large pot full of water to a boil. Add some salt and blanch the green beans until crisp tender, about 4 minutes. Transfer to an ice bath, then drain and pat dry. Place the green beans on a platter.
In a small pan over medium heat, add the 'nduja and the remaining teaspoon of olive oil. Cook, breaking up with a spoon, until fat is rendered and meat is crisp, about 5 minutes. Add shallots and cook until translucent, about one minute more. Remove from heat. Stir in sherry vinegar.
To assemble the dish, place the beans on a large platter. Drizzle with 'nduja vinaigrette and top with cornbread croutons.