Peel and chop the potatoes into even chunks. Place them in a saucepan, cover with salted water, and bring to a boil. Cook until very tender, about 15 minutes, then drain well.
While the potatoes cook, dice the onion and mince the garlic. Heat oil in a large skillet over medium heat, then sauté the onion until translucent and fragrant, about 5 minutes.
Add the minced garlic to the skillet and cook for another minute until it smells sweet and fragrant.
Add the chopped leftover roast vegetables to the skillet. Cook, stirring occasionally, until they caramelize slightly and develop a smoky aroma, about 10 minutes. Season with salt, pepper, and Worcestershire sauce.
Push the vegetable mixture to one side of the skillet. Add the ground lamb to the cleared space and brown, breaking it apart with your spoon, until fully cooked and browned, about 8 minutes. Mix everything together.
Drain the cooked potatoes and return them to the saucepan. Mash with butter and milk until smooth, fluffy, and creamy. Stir in smoked paprika for a smoky flavor.
Transfer the meat and vegetable filling into your baking dish, spreading it evenly. Top with the mashed potatoes, smoothing the surface with a spatula.
Bake in a preheated oven at 200°C (390°F) for 20–25 minutes, until the top is golden and crispy, and the filling is bubbling around the edges.
Remove from the oven and let rest for 5–10 minutes, allowing the filling to set and making it easier to serve. Scoop out portions and enjoy your hearty, smoky shepherd’s pie.
