Peel and chop the potatoes into even chunks (about 1-inch pieces) and place them in a pot.

Cover with salt water, bring to a boil, and simmer for about 15-20 minutes or until easily pierced with a fork.

Drain the potatoes and return them to the pot. Add the milk, butter, salt, and pepper, and mash until smooth and creamy.

In a large skillet, heat the vegetable oil over medium heat. Add the sausages and cook, turning occasionally, until golden brown and cooked through (about 12-15 minutes).

In the same skillet, melt the butter and add the sliced onions. Cook over medium heat until soft and caramelized (about 10 minutes).

Sprinkle in the flour and stir for a minute to cook it slightly.

Gradually pour in the beef broth and Worcestershire sauce, stirring constantly. Bring to a simmer until thickened, adding salt and pepper to taste.

On a plate, spoon a generous helping of mash, arrange the sausages on top, and drizzle the onion gravy over everything.