Preheat oven. Preheat oven to 400 degrees F. and spray a large casserole dish with non-stick cooking spray.
Cook the lamb and beef. Heat 1 tablespoon of olive oil in a large heavy-bottomed skillet over medium-high heat. Add the ground lamb and use a wooden spatula to break it apart into smaller pieces. Continue to cook until browned - approximately 5 minutes. Drain any excess fat and remove the ground lamb to a clean plate. Set aside.
Sauté the vegetables. To the same skillet add the remaining tablespoon of olive oil over medium-high heat. Add the onion and cook until soft, approximately 3-4 minutes. Stir often. Add the carrots and celery to the skillet and continue to cook for 4-5 minutes, stirring often. Add the minced garlic and sauté for 60 seconds, stirring continuously, before seasoning with salt, pepper, and Italian seasoning.
Sprinkle with flour and mix with tomato paste. Reduce heat to medium and sprinkle the vegetables with 3 tablespoons of flour, mixing thoroughly to incorporate the flour into the vegetables. Mix in the tomato paste, reducing heat if necessary to prevent it from burning.
Add broth and Worcestershire sauce and simmer. Slowly add the chicken broth and mix well to combine. Add the Worcestershire sauce and fresh chopped rosemary and bring to a simmer. Reduce heat to low and continue to cook for approximately 5 minutes.
Return the ground lamb and peas. Return the lamb to the vegetables and add the peas. Mix well to combine and cook for 2-3 minutes. Remove from heat.