Place the bacon in a large unheated skillet; cook over medium-low heat, turning occasionally, until just browned and crisp, about 10 minutes. Transfer the bacon to a cutting board using a slotted spoon, leaving the fat in the skillet.
Preheat the oven to 425ºF; place 2 rimmed baking sheets in the oven as it preheats.
Rub the chicken with 1 tablespoon of the avocado oil and toss the broccoli and garlic cloves with the remaining 2 tablespoons of oil; season both the chicken and broccoli moderately with salt and pepper. Spread the chicken on one hot baking sheet and the broccoli and garlic on the other. Roast until the chicken is cooked through and the broccoli is tender and lightly caramelized in spots, turning the chicken and stirring the broccoli once halfway through, 20 to 25 minutes (remove the broccoli sooner if it begins to brown too much).
Meanwhile, add the mushrooms to the skillet with the bacon fat and season lightly with salt. Raise the heat to medium and cook, stirring occasionally, until the mushrooms have released their water, 6 to 7 minutes. Add the onion, sprinkle with salt, and cook, stirring occasionally, until the onion is tender and the mushrooms are turning golden in spots, 6 to 7 minutes longer. Remove the pan from the heat and set aside.
In a large bowl, whisk together the mayonnaise, sour cream, lemon juice, chili powder, paprika, ¾ teaspoon of salt, and ¼ teaspoon of pepper. Add the riced cauliflower to the bowl.
When the chicken and broccoli are done, remove the pans from the oven and reduce the oven temperature to 375ºF. Transfer the chicken to a cutting board and allow to rest for 5 minutes; let the broccoli cool until it’s cool enough to handle, then coarsely chop it and add it to the bowl with the mayonnaise mixture. Squeeze the roasted garlic from the skins, mince the garlic, and add it to the bowl along with the onion and mushrooms. Chop the chicken; add it to the bowl, along with any juices that have accumulated on the cutting board. Add ¾ cup of the cheese. Chop the bacon and add it to the bowl. Fold all of the ingredients together. If the mixture is dry, stir in broth ¼ cup at a time until it is creamy.
Grease a 9 by 13-inch baking pan. Spread the chicken mixture evenly in the pan. Sprinkle with the remaining ¼ cup of cheese. Bake until the casserole is heated through, bubbling, and golden in spots, 20 to 25 minutes. Let stand for 5 minutes before serving.