Preheat your oven to 400°F.
Start by boiling the potatoes in a large pot until they're tender.
Once boiled, drain them and mash with half-and-half, butter, and egg yolk.
In a large skillet, heat the vegetable oil over medium heat.
Add the onions and carrots, cooking them until they start to soften.
Mix in the garlic and continue cooking for another minute.
Add the ground lamb to the skillet, seasoning with salt and pepper.
Cook everything together until the lamb is browned and cooked through.
Stir in the tomato paste followed by the chicken broth, Worcestershire sauce, and rosemary.
Let the mixture simmer until it's slightly thickened.
Spread the meat mixture evenly in a baking dish.
Top with the mashed potatoes, spreading them out to cover the meat completely.
Bake in the oven for about 30 minutes or until the top is golden brown.