Boil the potatoes in salted water until fork-tender, about 15-20 minutes. Drain well.
While potatoes are boiling, cook the sausages in a large skillet over medium heat until browned and cooked through. Remove sausages from skillet and set aside.
In the same skillet, add the sliced onions and cook until softened and slightly caramelized, about 5-7 minutes.
Sprinkle the flour over the onions and cook for 1 minute, stirring constantly.
Gradually whisk in the beef broth and Worcestershire sauce until smooth. Bring to a simmer and cook until the gravy thickens, about 5 minutes.
Mash the drained potatoes with the warmed milk, butter, salt, and pepper until smooth and creamy. Adjust seasoning as needed.
Serve the cooked sausages over the mashed potatoes, drizzled with the onion gravy.
Notes
This dish is best served immediately. You can add a splash of beer to the gravy for an extra layer of flavor.