Brown ground beef in the soup pot. While the beef cooks, slice the celery and carrots and cube the potatoes.
When the ground beef is browned and cooked through, remove from the soup pot, put into a bowl, and set aside. Leave the fat in the pot for sauteing the veggies. If there's not enough fat, melt about 1/2 tbsp. of butter.
Saute sliced celery in the beef fat or butter for 5 minutes, then add the carrots and saute for another 5-10 minutes.
Add the beef back into the pot, as well as the potato cubes. Pour in the vegetable and beef or chicken broths and diced tomatoes. Stir to combine.
Add the seasonings: sea salt, black pepper, Italian seasoning, celery seed, and bay leaves. Stir well to combine. (Note: the amount of salt you use will depend on how salted your broths are. Start with 1 tsp. and add more as needed.)
Bring the soup to a boil on high heat while uncovered and then turn down to low, placing the lid on the pot. Simmer on low heat for 20-30 minutes until the vegetables are soft but not mushy.
Add the frozen peas (or green beans) and simmer until cooked, about 5-10 minutes.
Serve alongside a salad or homemade bread.