Preheat your oven to 400°F (200°C) so it is hot and ready when the Shepherd’s Pie is assembled.

Place the peeled and chunked russet potatoes in a large pot, cover with cold water, and bring to a gentle boil over medium-high heat.

Reduce the heat to a simmer and cook the potatoes until they are very tender when pierced with a fork, about 15 to 20 minutes.

While the potatoes cook, heat the olive oil in a large skillet over medium heat.

Add the finely chopped yellow onion and diced carrots to the skillet and cook, stirring occasionally, until they begin to soften, about 5 minutes.

Stir in the minced garlic and cook for about 30 seconds, just until fragrant, being careful not to let it burn.

Add the ground lamb to the skillet, breaking it up with a spoon, and cook until it is no longer pink, about 6 to 8 minutes.

Season the lamb mixture with the salt, black pepper, dried thyme, and dried rosemary, stirring well to distribute the seasonings evenly.

Stir in the tomato paste until it coats the meat and vegetables, then sprinkle the all-purpose flour over the mixture and stir again to combine.

Pour in the beef broth and bring the mixture to a gentle simmer, stirring until the liquid thickens into a gravy-like consistency, about 3 to 5 minutes.

Stir the frozen peas into the lamb mixture and cook for 1 to 2 minutes, just until the peas are no longer icy but still bright green.

Remove the skillet from the heat and spread the lamb and vegetable mixture evenly in the bottom of a medium baking dish.

When the potatoes are tender, drain them well and return them to the warm pot.

Add the unsalted butter, whole milk, salt for the potatoes, and black pepper for the potatoes to the pot with the potatoes.

Mash the potatoes until they are smooth and creamy, adjusting the seasoning if needed to taste.

Spoon the mashed potatoes over the lamb mixture in the baking dish, spreading them gently to the edges to cover the filling completely.

Use a fork to lightly rough up the surface of the mashed potatoes to help them brown in the oven.

Place the baking dish in the preheated oven and bake for 20 to 25 minutes, or until the top is lightly golden and the filling is bubbling around the edges.

Remove the Classic Shepherd’s Pie from the oven and let it rest for about 10 minutes before serving so the layers can settle slightly.