Preheat the oven to 400 and retrieve a 9x12 or comparable baking dish.
Steam Cauliflower while sauteing the onion. Saute the onion until it is almost clear then add the beef and brown thoroughly. I season the meat here liberally with salt and pepper.
When the cauliflower is softened, transfer it to a food processor adding a large amount of butter or ghee. I tend to eyeball it but probably add about 4 TB. Process the cauliflower until it turns into a very soft whipped potato consistency. I'll season it with salt and pepper to taste and pulse it a few times to mix the seasoning well. Faux-tatoes complete! Taste and add seasoning or butter as needed.
Add the green beans (and carrots if you want) to the beef mixture for about 5 minutes. Then add the thyme and rosemary and mix well. I also season with more salt and pepper with the additional veggies added.
Add the broth, mix well, and cook for another 5 minutes mixing everything well.
Scrape the beef mixture into the baking dish and flatten out well. Then add the cauliflower to the top and smooth out like a cake frosting. Add additional chunks of butter across the top of the cauliflower. Then toss it in the oven for 40-45 minutes.