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In a nonstick skillet, heat the coconut oil over medium high. Once hot, add the onion and cook until beginning to soften, about 5 minutes. Add the ginger, garlic, curry, garam masala, chili powder, salt, and tomato paste. Cook until fragrant, about 30 seconds.
Transfer the onions to a 6-quart or larger slow cooker. Lay the chicken on top, then the cauliflower florets, and top with tomato sauce. Stir to combine the florets and sauce a bit, leaving the chicken pieces undisturbed underneath. The chicken pieces will seem large and a bit in the way. Just use a spoon to prod the sauce and florets around a bit so things are more evenly coated. Scatter the butter pieces over the top.
Cover and cook on high for 1 1/2 to 2 1/2 hours or on low for 4 to 6 hours, until the chicken is cooked through and reaches 165 degrees F on an instant-read thermometer. The cooking time may vary based on your slow cooker, so check early to ensure the chicken does not dry out. When the chicken is done, remove it to a cutting board and let cool slightly.
At this point, the cauliflower is not likely to be tender. Give the contents of the slow cooker a big stir to coat the florets with the sauce. Recover the slow cooker and cook on HIGH until the florets are completely tender, about 30 minutes to 1 hour more. (If your florets are already tender, you can skip this step.)
Once the chicken is cool enough to handle safely, cut it into bite-size pieces. Return to the slow cooker with the tender florets. Stir in the half-and-half. Let cool a few minutes, then stir in the Greek yogurt. (Don't stir in the yogurt right away; if the butter chicken is too hot, it will curdle.) Enjoy warm over brown rice, quinoa, or naan, sprinkled with fresh cilantro.