01 - Preheat your oven to 400°F.
02 - In a large skillet set over medium heat, warm the olive oil. Add the finely chopped onion, diced carrots, and diced celery; sauté for 5 minutes until they begin to soften.
03 - Incorporate the minced garlic and cook for 1 minute until fragrant. Add the ground lamb, cooking until thoroughly browned, using a spoon to break up the meat. Drain any excess fat if necessary.
04 - Stir in the tomato paste, Worcestershire sauce, fresh or dried thyme, fresh or dried rosemary, salt, and black pepper. Continue cooking for 1 to 2 minutes to allow the flavors to meld.
05 - Pour in the beef or lamb broth and bring the mixture to a simmer. Cook uncovered for 10 minutes, stirring occasionally, until the gravy has thickened to your desired consistency. Stir in the frozen peas, then remove the skillet from the heat.
06 - While the lamb filling simmers, place the peeled and chunked potatoes in a large pot. Cover them with cold, salted water and bring to a boil. Reduce heat and simmer for 15 to 20 minutes, or until the potatoes are fork-tender.
07 - Drain the cooked potatoes thoroughly and return them to the pot. Add the butter and warmed milk. Mash until the potatoes are smooth and creamy. Season with salt and pepper to taste. If desired, stir in the shredded Irish cheddar cheese until melted and combined.
08 - Transfer the prepared lamb mixture evenly into a 2-quart baking dish. Carefully spread the mashed potato topping over the lamb filling. Use a fork to create decorative ridges on the surface of the mashed potatoes for added texture and crispiness during baking.
09 - Bake the shepherd's pie for 25 to 30 minutes, or until the potato topping is golden brown and the filling is visibly bubbling. For an extra browned and crisp topping, broil for 2 to 3 minutes at the very end, watching carefully to prevent burning.
10 - Allow the pie to rest for 10 minutes after baking before serving to allow the filling to set.