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Rice the cauliflower using a food processor or box grater. (Learn more about how to make cauliflower rice here.)
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Heat the oil in a large saute pan over medium-high heat. Add the cauliflower rice and sea salt. Stir fry until the cauliflower is cooked and a little browned, about 7-10 minutes.
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Remove from heat. Stir in the cheddar cheese and heavy cream.
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Transfer the mixture evenly to a 9 x 13 in (23 x 33 cm) glass casserole dish. Set aside.
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Preheat the oven to 400 degrees F (204 degrees C).
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Lightly wipe down the saute pan to remove any cauliflower pieces, and add the ground beef. Season with sea salt and black pepper. Cook the ground beef until browned, about 10 minutes. Drain if needed.
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Sprinkle the ground beef evenly over the cauliflower in the casserole dish.
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Drizzle the casserole with ketchup (you can make your own sugar-free ketchup like this, or store bought is fine if you are not strictly sugar-free) and mustard. Sprinkle with shredded cheese.
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Bake for about 10 minutes, until casserole is hot and cheese melts.