Preheat the oven to 400°F. Boil the potatoes in a large pot of salted water until fork-tender, about 15 minutes. Drain and return them to the pot.
Mash the potatoes with butter, milk, and 1 cup of the sharp cheddar until smooth. Set the mash aside while you prepare the filling.
In a large skillet over medium heat, cook the ground beef until browned. Add the onion and carrots and cook for 5 minutes until they begin to soften.
Stir in the garlic, tomato paste, beef broth, Worcestershire sauce, salt, and pepper. Simmer for 5 minutes until the liquid thickens slightly. Add the peas and cook for 2 more minutes.
Spread the beef mixture evenly in a baking dish. Spoon the cheddar mashed potatoes over the top and smooth it out. Sprinkle the remaining 1/2 cup cheddar and the crumbled bacon across the surface.
Bake for 20 minutes until the top is golden and the edges bubble. Remove from the oven and scatter the chives over the finished pie before serving.