Begin by boiling the potatoes. Place the cubed potatoes in a large pot, cover with water, and add 1 teaspoon of salt. Bring to a boil and cook until tender, about 15-20 minutes. Drain and return to the pot.

While the potatoes are boiling, cook the sausages in a large skillet over medium heat until browned and cooked through, about 10-12 minutes. Remove the sausages from the skillet and set aside.

In the same skillet, add the sliced onions and cook over medium heat until they are soft and caramelized, about 10-15 minutes.

Sprinkle the flour over the onions and stir to combine. Cook for an additional 1-2 minutes to eliminate the raw flour taste.

Gradually add the beef broth while stirring, then add the Worcestershire sauce. Bring the mixture to a simmer and cook until thickened, about 5 minutes. Season with salt and pepper to taste.

While the gravy is thickening, mash the drained potatoes with 3 tablespoons of butter and the milk until smooth and creamy. Season with salt to taste.

Slice the cooked sausages and return them to the skillet with the onion gravy. Stir to coat the sausages in the gravy.

Serve the sausages and onion gravy over a generous scoop of mashed potatoes. Garnish with chopped parsley if desired.