In a large Dutch oven saute the onion in about 3 tablespoons olive oil on medium-high heat, and when it is completely softened, and before it starts browning, add the garlic. Saute for an additional couple of minutes, then add the peppers, lower the heat to medium-low and stir well. Partially cover with a lid and let them soften up, about 10 minutes.
When the peppers have settled into the pan, add the tomatoes and the potatoes. Season the mixture with salt and pepper to taste, stir well over medium-low heat, cook for about 1 hour.
Use the vegetable stock to help the sauce come together, by adding a ladleful to the peperonata here and there while cooking. Depending on the tomatoes you are using and the degree of ripeness of the peppers, you might not need to use all the broth indicated in the ingredient list. Look for a nice balance between sauce and vegetables, at the end you are working on a vegetable stew...consistency of the final dish should be thicker than a pasta sauce.