Add the potatoes to a pot of cold salted water.

Bring water to a boil and cook the potatoes for about 20 to 25 minutes more, or until tender.

Drain the potatoes, then mash with butter and milk. Season with salt and pepper to taste.

Add 1 tbsp of butter to a braiser or deep oven safe sauté pan set over medium heat. Add the vegetables and thyme and cook for 5 minutes. Season with salt and pepper.

Add the beef, season with salt and pepper, and cook for 7 minutes or until almost cooked through.

Make a well in the center of the pan and add 1 tbsp of butter, then mix in the flour and cook for 1 minute.

Mix in the tomato paste, Worcestershire, and broth.

Bring the sauce to a boil, then reduce the heat to a simmer and cook for 15 to 20 minutes until the sauce thickens and becomes more of a gravy.

While the gravy is cooking, preheat the oven to 375°F.

Top the meat and vegetables with the prepared mashed potatoes, using a fork to even them out and carefully spread the potatoes to the edges.

Top the mashed potatoes with parmesan.

Bake for 20 minutes then broil on high for 2-3 minutes until golden brown.

Garnish with chives.