In a large skillet, heat the vegetable oil over medium heat.
Add the sausages and cook, turning occasionally, until browned and cooked through, about 15-20 minutes.
Remove the sausages from the skillet and set aside. Keep warm.
While the sausages are cooking, place the potatoes in a large pot and cover with water.
Bring to a boil, then reduce the heat and simmer until the potatoes are tender, about 15-20 minutes.
Drain the potatoes and return them to the pot.
Add the milk and butter, and mash until smooth and creamy.
Season with salt and black pepper to taste. Keep warm.
In the same skillet used for the sausages, melt the butter over medium heat.
Add the sliced onions and cook, stirring occasionally, until they are soft and caramelized, about 10-15 minutes.
Sprinkle the flour over the onions and cook, stirring constantly, for 1-2 minutes.
Gradually add the beef broth, stirring constantly to prevent lumps.
Add the Worcestershire sauce and bring the mixture to a simmer.
Cook until the gravy has thickened, about 5-10 minutes.
Season with salt and black pepper to taste.
Divide the mashed potatoes among plates.
Top with the sausages.
Spoon the onion gravy over the sausages and mashed potatoes.
Enjoy your meal!