Preheat the oven to 450 degrees ;. In a large saucepan, combine the potatoes and enough salted water to cover by 1 inch. Bring to a boil; cook until crisp-tender, about 20 minutes. Using a slotted spoon, transfer to a colander. Add the green beans to the boiling water; cook, stirring, for 2 minutes. Drain in the colander with the potatoes; let cool.
Meanwhile, form the sausage into 1-inch balls and place in a shallow baking dish. Bake, turning occasionally, until browned, 15 to 20 minutes.
Halve the potatoes and season with salt and pepper. Arrange the potatoes, green beans, meatballs, tomatoes and bread cubes in serving bowls.
In a small, heavy saucepan, whisk together the chicken broth and cornstarch and bring to a boil over medium heat. Add the cheese, remove from the heat and stir until melted. Sprinkle with the chili powder and serve with the vegetables, meat and bread for dipping.