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. Scatter the butter pieces over the top.

Cover and cook on high for 1 ½ to 2 ½ 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.

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.

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 (or coconut milk). Let cool a few minutes, then stir in the Greek yogurt.