Preheat oven to 375°F/190°C.
Cut raw chicken breast into small cubes.
Preheat skillet then add 1 tablespoon of olive oil and chicken cubes. At medium heat, cook chicken, stirring occasionally until cooked, about 7-10 minutes.
Cut bell peppers in half (horizontally) and remove seeds and ribs. Lay pepper halves cut side up in a microwave-safe dish with 1/4 cup water in the bottom. Lightly sprinkle insides of pepper halves with kosher salt. Cover and microwave peppers until softened, about 5-10 minutes. Drain water from pan and set aside.
In a large skillet or dutch oven, sauté onions and celery with other tablespoon olive oil and a pinch of salt over medium heat until they begin to soften, about 4-5 minutes.
Add cremini mushrooms and cook until mushrooms soften, about 5-7 minutes, then transfer to bowl.
In the same dutch oven or skillet, melt butter over medium heat, scraping bits from bottom of pan if there are any. Whisk in almond flour and cook over low heat for 2-3 minutes, stirring constantly so flour taste cooks out and mixture becomes lightly browned.
Add chicken stock and almond milk to the butter-almond flour mixture, stirring constantly to avoid lumps.
Add thyme (crushing it between your fingers), ground mushroom powder, salt, and pepper.
Bring mixture to boil then reduce to medium heat and cook until sauce thickens and reduces by one third.
Add mushroom mixture back into the pan, along with cooked chicken cubes and cauliflower rice. Cook until warmed. Add more almond milk if sauce is too thick.
Place peppers in a baking dish with skin side down and fill pepper cavities with chicken mixture. Top each pepper with small handful of shredded cheese. Place any extra filling around the peppers. Cover with foil and bake for 20 minutes, or until bubbling and cheese is melted. Rest for 5 minutes and serve.