Boil water in large pot with 2 tablespoons salt. When water is boiling, put in the potatoes and boil for about 15 to 20 minutes, or until soft.

Melt 6tbsp of butter. Drain, peel, then mash hot potatoes until smooth. Mix in the hot butter with 1/2 cup milk, until blended.

Melt the remaining 2tbsp butter in a large oven-safe skillet or pot over low/medium heat. Add in onions, carrots, garlic, thyme and rosemary. Stir until onions and carrots are quite tender. Add in beef and lamb while breaking the meat apart.

Add the tomato paste and stir for 2 to 3 minutes. Sprinkle the flour over the mixture and cook for 1 minute. Add the 3/4 cup beef stock and stir until the liquid has thickened slightly.

Stir in the parsley and remove the thyme and rosemary stems. Season to taste with salt and pepper. Keep in mind that the beef stock is already salty. Turn off heat.

Heat up the oven to 375F or 191C. Spread the meat evenly, then top it off with the potatoes, spreading evenly. Lastly, add the shredded cheddar on top. If necessary, place a foil-lined baking sheet underneath the pan to catch any drips.

Bake the pie until the potatoes have begun to brown and the edges are bubbling, about 30 minutes. Let stand at room temperature for 15 minutes before serving.