In a large pot, filled halfway with water and 1 tbsp of kosher salt, bring to a boil over high heat. Once boiling, add the potatoes in for 10-15 minutes until easy pierced with a knife soft.
While the potatoes are boiling, in a small saucepan add the butter and milk over low-medium heat. Let the butter melt and the milk warm together.
Drain water from potatoes and return to the pot, removed from heat. Mash the potatoes using a masher or a ricer. Do not use an immersion blender or the potatoes will become gummy in texture. Once mashed, mix in the hot butter/milk, 1/4 tsp kosher salt, 1/4 tsp black pepper, and grated parmesan cheese.
Mix together until just incorporated, do not over mix or it will affect the texture. Taste and adjust seasoning if necessary. Cover and set aside.
Preheat oven to 375F.
In a 10-12 inch cast iron skillet over medium high heat, add 2 tbsp of olive oil. Add in the diced onion and carrots, and saute for 8 minutes, until onions and carrots begin to soften.
Add in the ground lamb and break it apart as it cooks for 2 minutes. Add in the chopped rosemary, thyme, grated garlic, 1/2 tbsp kosher salt, 1/2 tbsp ground black pepper. Continue to cook for 6-8 minutes until the meat is browned and cooked through.
Pour in the red wine and allow the pan to deglaze until the liquid reduced by half (about 2-3 minutes). Add in the 2 tbsp of Worcestershire sauce and the tomato paste. Stir to combine and cook for 2-3 minutes. Add in the frozen peas and stir to combine.
Remove from heat, Taste and adjust salt and pepper if necessary.
Add dollops of potato mash over the top of the meat mixture and using the back of a spoon or fork, smooth over the top to cover all of the meat. Take the melted tbsp of butter and brush over the top of the potatoes.
If your cast iron is very full, place it on a sheet pan before putting it in the oven to catch any drips.
Place into the oven and bake for 30 minutes. If needed, broil on high at the end for 2-3 minutes or until the top is browned.
Let cool for 10-15 minutes before serving to allow the inside to set. Top with fresh parsley to serve.