Preheat he oven to 350 degrees F and adjust the rack to the middle position. Heat the butter in a large skillet over medium heat. Add the onion and mushrooms and sauté until the mushrooms are soft and have released their juices, about 10-12 minutes. Move the vegetables to the side of the pan and add the garlic and thyme in the center of the pan. Stir the garlic and thyme until fragrant, about 45 seconds, then stir them into the mushroom mixture. Turn off the heat and stir in the shredded turkey, cream, 1 1/2 tsp sea salt, and pepper. Pour the mixture into an 8×8-inch baking dish.
To make the biscuit topping, place the almond flour, coconut flour, sea salt, baking soda and baking powder into the bowl of a food processor. Pulse 2-3 times to combine. Add the butter and pulse for eight 1-second pulses. Pour in the milk and pulse until the mixture comes together and forms a dough. Use a 2-inch cookie scoop to scoop out the dough balls and place them on top of the chicken filling, lining up the balls in a symmetrical pattern. Bake for 25-30 minutes until the filling is bubbly and the biscuits are golden brown on top. Cool for 10 minutes before serving.