Preheat your oven to 400°F (200°C). Grease your muffin tin lightly with butter or oil to prevent sticking.

Heat 1 tablespoon of vegetable oil in a frying pan over medium heat. Add the sausages and cook until browned and cooked through, about 10-12 minutes, turning occasionally. Let cool slightly, then slice lengthwise into halves or thirds.

Place peeled and chopped potatoes in a large pot, cover with cold water, add a pinch of salt, and bring to a boil. Cook until tender, about 15-20 minutes. Drain well.

While still hot, mash potatoes with butter, milk, thyme, salt, and pepper until creamy and smooth but not runny. Adjust seasoning to taste.

Take a spoonful of mashed potatoes and press it into each muffin cup, forming a thin, even layer on the bottom and sides to create a cup.

Place a slice or two of browned sausage inside each potato cup, pressing gently to fit snugly.

Add another spoonful of mashed potatoes on top, smoothing it out. Optionally, sprinkle grated cheddar cheese on top.

Bake in the oven for 15-20 minutes, or until the edges of the potato cups turn golden and crispy.

Let the cups cool slightly before removing from the tin. Garnish with fresh parsley or chives if desired.