Place a large, deep, non-stick pan (or even medium non-stick pot) over medium-high heat, and add in about 1 tablespoon of oil; once the oil is hot, add in the smoked sausage medallions, and caramelize them for a few minutes until they become a deep brown color; remove the sausage from the pan with a slotted spoon, and set aside.

-To the same pan or pot, add in the butter, and allow it to melt; add in the sliced onions, and caramelize those in the butter and sausage drippings until a rich, golden-brown, about 5-7 minutes; next, add in the garlic, plus a couple of pinches of salt, the freshly cracked black pepper and the paprika, and stir to combine with the onions; saute just until the garlic becomes aromatic.

-Next, add in the sliced potatoes, and fold them into the caramelized onions/garlic to coat them well; add in the chicken stock and stir to combine, then push the sliced potatoes down into the stock/onion mixture as much as possible to allow them to cook evenly; cover the pan/pot with a lid that is askew to allow some steam to escape, and simmer on medium-low heat for about 15 minutes, stirring gently once or twice during this time; then, uncover the pan/pot and allow the potatoes to continue to simmer for another 10 minutes, or until they are tender and the sauce a bit thickened, stirring once or twice during that time. (It’s perfectly fine for some of the potatoes to break up in the sauce as it helps to thicken it, just take care not to break them too much.)

-Finish the Goulash by adding the caramelized smoked sausage back into the pan/pot, as well as the parsley, and gently fold those in to incorporate; add a little drizzle of olive oil in, and add a couple more pinches of salt and pepper, if necessary; serve hot with bread, if desired.