Preheat oven to 400 degrees F.
Toss the sweet potato cubes with 1 tbsp melted butter, salt, and pepper, and bake for 15 minutes.
Meanwhile, heat a tbsp of butter in a large skillet over medium high heat.
Throw in onion slices, celery, and garlic into the skillet and sauté until the onions are soft.
Add the sausage to the pan and cook, breaking it up, until the meat is browned.
Pour out as much liquid as possible, and place the mixture into a 9x13 baking pan.
In the same skillet, heat another tbsp of butter.
Add mushrooms with salt and pepper to the pan and let them cook until they sweat out most of the liquid and become soft.
Add the apple cubes and sauté for 5 more minutes.
Pour the mixture into the baking pan with the sausage mixture.
Add chopped nuts and cooked sweet potato cubes to the mixture.
In a separate bowl, whisk together eggs, thyme, broth, and salt and pepper.
Pour into the baking pan.
Stir everything together to mix well.
Bake in the 400 degree F oven for 30 minutes.
Let cool for 10 minutes before serving.