In a Dutch oven, sauté the peppers in oil over medium-high heat, stirring until soften and nicely charred/browned on all sides, about 10 minutes. Transfer to a plate and set aside.
Add onions to pot, sautéing until golden brown. Add potatoes, broth and red peppers. Bring to a boil, reduce and simmer covered 15 minutes or until potatoes are tender.
Use a potato masher to coarsely mash the soup to your likeness, then stir in milk and cayenne pepper. Once heated throughout, remove from heat and stir in butter and parsley, season to taste with salt and pepper.
Notes
Using a heavy-bottomed pot like a Dutch oven allows you to brown foods without burning them.