Peel and cut russet potatoes into even chunks, then boil in generously salted water for 15–20 minutes, until tender and easily pierced with a fork. Drain thoroughly.

Return potatoes to the pot with butter and warmed milk, then mash until smooth, creamy, and lump-free. Season with salt and pepper.

Heat a large skillet over medium heat, add sausages in a single layer, and cook for 12–15 minutes, turning occasionally, until golden brown.

Add thinly sliced onions to the same skillet, cooking on medium-low heat for 10–12 minutes until golden and caramelized.

Sprinkle flour over the onions, stirring constantly for 1–2 minutes to cook out raw taste and create a smooth roux.

Slowly pour in stout, scraping up browned bits, and simmer until the liquid reduces by half, about 5 minutes.

Stir in stock, Worcestershire sauce, and fresh thyme; simmer for another 3–5 minutes until the gravy coats the back of a spoon.

Plate creamy mash onto warm plates, arrange sausages on top, and ladle rich gravy over everything.