Preheat oven to 400°F. Lightly grease a medium baking dish or oven-safe skillet.
Heat olive oil in a large skillet over medium heat. Add ground meat and cook until browned, breaking it up as it cooks.
Add onion and cook for 3 to 4 minutes, until softened. Stir in garlic and cook for 30 seconds.
Stir in tomato paste, Worcestershire sauce, salt, and pepper. Add frozen vegetables and broth. Simmer for 5 to 7 minutes until slightly thickened.
Transfer mixture to prepared baking dish and spread evenly.
Warm mashed potatoes slightly, then spread over filling.
Sprinkle cheese over the top.
Bake for 20 to 25 minutes, until golden and bubbling.
Let rest a few minutes. Top with chives before serving.