Preheat your oven to 375°F (190°C).
In a large skillet, heat the olive oil over medium heat. Add the diced onion and minced garlic, sautéing until the onion is translucent, about 3-4 minutes.
Add the sliced carrots and diced potatoes to the skillet, cooking for another 5 minutes until they begin to soften.
Stir in the frozen peas, dried thyme, dried rosemary, salt, and pepper. Mix well.
In a separate bowl, combine the chicken pieces with the diced tomatoes (with their juice) and chicken broth. Pour this mixture into the skillet with the vegetables.
Bring the mixture to a simmer, then reduce the heat and stir in the heavy cream. Cook for an additional 5 minutes.
Transfer the mixture to a greased 9x13 inch casserole dish.
Sprinkle the shredded cheddar cheese evenly over the top, followed by the breadcrumbs.
Bake in the preheated oven for 25-30 minutes, or until the top is golden brown and bubbly.
Let it cool for about 5 minutes before serving.