Heat oil in a skillet over medium high heat. Add sausages and stout. Cover with lid and crack just to allow enough steam to escape. Cook covered for about 10 minutes, turning half way through. After they're cooked for 10 minutes, remove lid and allow liquid to reduce a bit and coat sausages. When the liquid is almost gone, lower heat to medium low and continue cooking with the lid on, rotating occasionally, until evenly browned and cooked through, about 10 minutes.
In a separate pot, heat butter over medium high heat. Add sliced onions and cook until slightly browned and fragrant, about 5 to 10 minutes. Sprinkle with flour and allow to cook 2 to 3 minutes. Add stout and scrape bottom of pan to deglaze. Add beef broth and allow to simmer until no longer foamy; 10 to 15 minutes.
In a large pot, cover potatoes with water and bring to a boil.
Cook until soft, drain, add butter and milk. Mash to your preferred consistency.