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1
Preheat the oven to 375 degrees F (190 degrees C).
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2
Place olive oil and butter in Dutch oven over medium heat. Stir in onion and ground lamb; brown the meat, breaking it up into small crumbles as it cooks, about 10 minutes.
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3
Stir in flour until incorporated, then mix in salt, black pepper, rosemary, paprika, cinnamon, ketchup, and garlic; cook and stir until garlic is fragrant, 2 to 3 minutes.
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4
Stir in water and scrape up any brown bits from the bottom of the Dutch oven. Reduce heat to medium-low and bring mixture to a simmer; cook and stir until thick, about 5-6 minutes.
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5
Remove lamb mixture from heat and stir in peas and carrots until combined.
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6
Spread lamb mixture into the bottom of a 9x13-inch baking dish and set aside.
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7
Place potatoes into a large pan of salted water. Bring to a boil, reduce heat to medium, and cook until tender, about 15 minutes. Drain well and return potatoes to pan.
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8
Mash butter, cayenne pepper, cream cheese, and Irish cheese into the potatoes. Mash until combined and potatoes are smooth. Season to taste with salt and black pepper.
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9
Whisk together egg yolk and milk in a small bowl; stir into the mashed potato mixture.
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10
Top the lamb mixture in the baking dish with the mashed potatoes and spread evenly to cover.
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11
Bake in the preheated oven until the top is golden brown and sauce is bubbling up around the edges, 25 to 30 minutes.
