In a large skillet over medium-low heat, melt the butter. Add diced onion and minced garlic, cooking until onion is translucent and garlic is fragrant. Stir in frozen peas and carrots, along with thyme and rosemary.
Add ground beef to the skillet, cooking until browned. Drain excess grease, then season with salt and pepper. Stir in beef broth, Worcestershire sauce, and tomato paste. Simmer for 5 minutes.
Spoon the prepared mashed turnips on top of the filling.
Bake in the preheated oven for 25 to 35 minutes, or until the top is golden brown and slightly crisp.