Boil water in a large pot over medium high heat.
Add the carrots and simmer for 5 minutes.
Add in the cauliflower florets and cook for 5 more minutes until both the carrots and the cauliflower are cooked through and fork tender.
Drain, and place in a food processor. Add ghee and salt, and process until everything turns smooth.
Preheat oven to 400 degrees F.
Heat ghee in a large oven-safe skillet over medium high heat.
Add onion, celery, and carrot, and cook stirring for 5 minutes.
Add minced garlic and stir for 1 minute until fragrant.
Add the ground beef with salt and pepper, and cook until browned (~7 minutes), breaking it up with a wooden spoon. Stir in tomato paste.
In a separate bowl, whisk together broth, apple cider vinegar, rosemary, thyme, and arrowroot starch.
Pour over the beef and simmer for 5 minutes until the sauce reduces and thickens.
Remove from heat, then top with mashed carrot and cauliflower, spreading it out evenly and smoothly over the meat mixture with a spatula.
Bake for 20 minutes in the oven until the topping turns golden brown and the meat layer starts bubbling up.
Cool for 10 minutes before serving.