01 - Preheat your oven to 400°F.
02 - In a large skillet over medium heat, warm the olive oil. Add the chopped onion, diced carrots, and celery; sauté for 5 minutes until they have softened.
03 - Add the minced garlic and cook for 1 minute more. Introduce the ground lamb to the skillet; cook until it is thoroughly browned, breaking up the meat with a spoon as it cooks. If necessary, drain any excess fat.
04 - Stir in the tomato paste, Worcestershire sauce, fresh or dried thyme, fresh or dried rosemary, salt, and pepper. Continue to cook for 1-2 minutes, allowing the flavors to meld.
05 - Pour in the beef or lamb broth and bring the mixture to a simmer. Allow it to simmer uncovered for 10 minutes, stirring occasionally, until the gravy has visibly thickened. Finally, stir in the frozen peas and then remove the skillet from the heat.
06 - While the lamb filling is simmering, place the peeled and chunked potatoes in a large pot. Cover them with cold, salted water and bring to a rolling boil. Reduce the heat and simmer for 15-20 minutes, or until the potatoes are tender enough to be easily pierced with a fork.
07 - Drain the cooked potatoes thoroughly and return them to the pot. Add the unsalted butter and warmed whole milk. Mash the potatoes until they are smooth and creamy. Season with salt and pepper to your preference. If desired, stir in the shredded Irish cheddar cheese.
08 - Transfer the prepared lamb mixture into a 2-quart baking dish. Carefully spread the mashed potatoes evenly over the top of the lamb filling. Use a fork to create decorative ridges on the potato surface; this will help them crisp up during baking.
09 - Bake the shepherd's pie in the preheated oven for 25-30 minutes, or until the potato topping is golden brown and the filling is visibly bubbling around the edges. For an even crispier and more golden crust, you may broil it for 2-3 minutes at the very end, watching carefully to prevent burning.
10 - Allow the shepherd's pie to rest for 10 minutes after baking before portioning and serving. This helps the filling set and prevents it from falling apart.