MAKE THE MASHED POTATOES:
Bring a large pot of generously salted water to a boil. Add the chopped potatoes and cook for 15 to 20 minutes, until fork-tender.
Drain the potatoes and let them steam dry in the pot for 1 to 2 minutes.
Into a large bowl, pass the potatoes through a potato ricer or mash until very smooth.
Add the butter and mix until fully melted in.
Pour in the warm half and half, then season with salt to taste and fold in Parmesan. Cover and set aside.
MAKE THE MEAT FILLING:
Preheat the oven to 400°F.
Melt the butter with the olive oil in a large skillet over medium heat.
Add the diced onion and sauté for 5 to 7 minutes, until soft and lightly golden.
Add the garlic and cook for another minute, until fragrant.
Stir in the tomato paste, thyme leaves, and finely chopped rosemary and cook for 1 to 2 minutes.
Add the ground lamb and cook for 7 to 9 minutes, breaking it up, until browned through.
Sprinkle in smoked paprika, red pepper flakes, salt, and black pepper and stir well.
Stir in the Worcestershire sauce.
In a small bowl, whisk together the beef broth and cornstarch, then pour it into the skillet. Simmer for 2 to 3 minutes, until thickened.
Stir in the peas and carrots and parsley and cook for 2 to 3 minutes, until heated through. Remove from the heat.
ASSEMBLY AND BAKING:
Spread the meat filling evenly into a baking dish.
Top with mashed potatoes using one of these methods. Pipe decorative dollops using a piping bag or spread evenly and drag a fork across the surface to create lines.
Brush the tops of the mashed potatoes with the melted butter.
Transfer into the oven with a tray underneath for any drippings. Bake for 25 minutes or until golden and crispy on top.
Switch the oven to broil and broil for 1 to 3 minutes, watching closely, until the top is golden and crisp.
Take out of the oven and sprinkle chopped fresh chives over the top before serving.