Peel and chop the potatoes into even chunks.
Boil the potatoes in salted water until tender, about 15 minutes.
While the potatoes cook, heat a skillet over medium heat and add the sausages.
Cook the sausages for about 12-15 minutes, turning occasionally until browned.
In another pan, melt 2 tablespoons of butter and add the sliced onion.
Sauté the onions until they are golden brown.
Sprinkle flour over the onions and stir to combine, cooking for 1 minute.
Gradually add the broth, stirring continuously until the sauce thickens.
Add Worcestershire sauce, salt, and pepper to taste.
Drain the potatoes and mash them with the remaining butter and milk until creamy.
Serve the sausages on a bed of mash, topped with onion gravy.