Preparation:

Step 1: Cook the Sausages

1. Heat a large frying pan over medium heat and add the olive oil and butter.
2. Add the sausages and cook, turning occasionally, until browned on all sides and fully cooked through, about 12-15 minutes.
3. Transfer the sausages to a plate and cover with foil to keep warm.

Step 2: Make the Onion Gravy

1. In the same pan used for the sausages, add the butter and olive oil.
2. Add the sliced onions and cook over medium heat, stirring frequently, for about 10-15 minutes until they soften and turn golden brown.
3. Sprinkle the flour over the onions and stir well to coat.
4. Gradually add the beef broth, whisking constantly to prevent lumps.
5. Stir in Worcestershire sauce, Dijon mustard (if using), salt, pepper, and thyme.
6. Simmer for about 5-7 minutes until the gravy thickens.
7. Taste and adjust seasoning as needed. Set aside.

Step 3: Prepare the Mashed Potatoes

1. Place the peeled and chopped potatoes in a large pot of salted water.
2. Bring to a boil and cook for about 15-20 minutes until potatoes are fork-tender.
3. Drain the potatoes and return them to the pot.
4. Add the butter, milk (or cream), salt, and black pepper.
5. Mash the potatoes until smooth and creamy.
6. Adjust seasoning if necessary.

Step 4: Assemble the Dish

1. Spoon a generous portion of mashed potatoes onto a plate.
2. Place the sausages on top of the mash.
3. Pour the rich onion gravy over the sausages and potatoes.
4. Garnish with fresh parsley if desired.