Make the potatoes. Peel and cube potatoes. Put in a large pot with cold water to cover by an inch. Partially cover the pot and bring to a boil over a high flame. Season generously with salt, reduce heat to simmer and cook, partially covered, until just tender, about 15 minutes.
Drain and return potatoes to pot. Briefly return to heat to cook off excess moisture. Using a hand masher, mash in the butter. (Do this before adding the buttermilk—for some scientific reason I can't dredge up right now, this makes them taste more buttery and keeps them from having a gluey texture.) Mash in the buttermilk and adjust seasoning with salt. Set aside.
Make the lamb filling. While the potatoes are cooking, preheat oven to 375ºF. Heat olive oil in a deep, large skillet or sauté pan over medium flame. Add onion and sauté, stirring frequently, until starting to soften, about 3 minutes. Add lamb to pan. Season generously with salt and pepper, and cook, breaking it up with a wooden spoon, about 5 minutes.
Clear a space in the middle of the pan and add thyme, rosemary and garlic. Cook, stirring until fragrant, about 45 seconds. Stir to combine and clear another space in the middle. Add tomato paste and cook for a minute or two, mashing against the bottom of the pan to brown it slightly. Sprinkle flour over the lamb and stir to combine everything. Add broth and cook, stirring occasionally, until liquid slightly thickens, 5 to 7 minutes. Stir in peas and carrots, and remove from heat.
Assemble and bake the dish. Spoon lamb filling into a 3-quart casserole, flattening out evenly across the bottom. Top with mashed potatoes, spreading them evenly over the lamb. Make sure to spread them to the edges of the casserole—this will minimize the filling bubbling out on the sides (it probably won't eliminate it, but that's okay). Some recipes have you drag a fork across the top of the potatoes to create an easily brownable surface. I did this, but you don't need to.
Transfer casserole to a rack in the center of the oven and bake until the potato topping is lightly browned, 30 to 35 minutes. If it doesn't brown to your liking, you can pop the casserole under the broiler for 2 or 3 minutes. I did this.
Remove from oven and let cool 5 to 10 minutes before serving.