"Create a dairy-free, wheat-free, corn-free, and pepper-free version of Chef John's Chicken a la King inspired by the linked recipe. Keep it beginner-friendly, quick/easy (15-30 min if possible), minimal processing, and suitable for a household of 3. Use imperial units only. Avoid all dairy, gluten/wheat, corn, soy, sesame, nuts, and shellfish. Do not include any peppers (bell peppers or black pepper). Make it creamy without dairy, likely using a safe alternative such as unsweetened coconut milk or another allergy-safe option, and keep the flavor mild and comforting. Include chicken, mushrooms, and peas if appropriate, but ensure all ingredients are safe and clearly labeled. Provide concise steps and a short note for serving suggestions."