Special equipment: 1 (9 by 5-inch) loaf pan
Preheat the oven to 350 degrees F.
Put the butter into a 4-quart pot and place over medium heat. When the butter has melted, add the onion, garlic and thyme sprigs. Saute until translucent, about 10 minutes. Add the mushrooms to the pot, stir, and raise the heat a bit. Cook the mixture until the liquid has cooked off, about 15 to 20 minutes. Remove from the heat and set aside.
Meanwhile, crack the eggs into a large bowl and whisk well. Add the cream, parsley and Cajun seasoning and whisk to combine. Add the mushroom mixture 1 serving spoonful at a time to temper the egg mixture, stirring well after each addition. Add the breadcrumbs and stir well.
Spray the loaf pan with nonstick spray, line with parchment paper, and pour the mixture into the pan. Set in a large roasting pan and fill the pan with water halfway up the loaf pan. Place into the top half of the oven and bake until the center is set, about 60 to 70 minutes. Remove from the oven and let cool 15 minutes before turning out onto a plate to slice.