Bring a pot of water to a full boil. Add the chopped potatoes and cook at a full boil for 15 to 20 minutes, until potatoes are very soft when poked. Strain water and allow potatoes to cool slightly.
Sauté the onions and carrots in oil over medium heat until softened but still al dente, about 8 to 10 minutes.
Move the veggies off to one side of the skillet, and add the ground lamb, minced garlic, dried oregano and thyme and continue cooking just until lamb meat has browned, about 2 minutes.
Stir in the flour and cook for 1 minute.
Pour the beef broth into the skillet and bring to a full boil.
Cook un-covered for 15 to 20 minutes, stirring occasionally, until mixture is very thick. Taste the mixture for flavor and add sea salt if desired.
Mash the cooked potatoes with buttermilk and sea salt until it reaches your preferred consistency. If you'd like, add grated parmesan or asiago cheese to the mashed potatoes, and if need be, add more buttermilk.
Preheat the oven to 400 degrees F.
Pour the lamb mixture into a 13" x 9" casserole dish (or a casserole dish that holds at least 1.5 quarts).
Spread the pureed potatoes on top of the lamb mixture. Place casserole dish on a baking sheet and bake on the center rack for 30 minutes, until shepherd's pie is bubbly and the potatoes are golden brown on top.
Remove shepherd's pie from the oven and allow it to cool for at least 10 minutes before serving. Note that the longer the pie sits, the thicker it will become.
Serve heaping portions of shepherd's pie with Irish Soda Bread.