Combine mashed potatoes, sour cream, cream cheese, 1 tablespoon butter, egg yolk, 1/2 teaspoon salt, and 1/2 teaspoon black pepper in a bowl.

Mix until the potato mixture is smooth.

Heat olive oil in a cast iron skillet or nonstick pan over medium-high heat.

Add ground lamb to the skillet and reduce heat to medium.

Cook the lamb, stirring frequently, until browned and crumbly (about 4-5 minutes).

Drain off any excess grease from the skillet.

Season the lamb with salt and black pepper to taste.

Add stewed tomatoes with juice, chopped onion, and chopped carrot to the ground lamb.

Simmer the mixture until the vegetables are tender (about 5-10 minutes).

Add peas to the lamb mixture and reduce heat to low.

Cook, stirring frequently, until the peas are warmed through (about 2-3 minutes).

In a separate saucepan, heat the Irish stout beer over medium heat.

Add the beef bouillon to the beer.

Cook and stir until the bouillon is dissolved (about 5 minutes).

In another pan, heat the remaining 1 tablespoon butter over medium-low heat until sizzling.

Whisk the all-purpose flour into the melted butter until a thick paste forms (about 1 minute).

Stir the beer mixture and Worcestershire sauce into the flour mixture until the gravy is smooth and thickened (about 2-3 minutes).

Stir the gravy into the lamb mixture and simmer until the mixture is thickened (at least 5 minutes).

Set the oven rack about 6 inches from the heat source and preheat the oven's broiler.

Grease a 9x12-inch baking dish.

Pour the lamb mixture into the prepared baking dish.

Carefully spoon the mashed potatoes over the lamb mixture, covering it like a crust.

Sprinkle the shredded cheddar cheese, chopped fresh parsley, and smoked paprika over the mashed potatoes.

Broil in the preheated oven until the crust is browned and the cheese is melted (about 4-5 minutes).

Cool for about 5 minutes before serving.