Preheat the oven to 375 degrees F and butter a 3-quart baking dish. Melt 8 tablespoons butter in a large skillet over medium heat. Add the onions, apples and thyme, season with salt and pepper and cook, stirring, until the onions are soft, about 3 minutes. Add the almonds, walnuts, sunflower seeds, dried blueberries and dried cranberries. Add the broth and bring to a simmer.
Whisk the eggs and parsley in a large bowl. Add the bread, then pour in the broth mixture and toss.
Transfer the stuffing to the prepared baking dish and dot with the remaining 1 tablespoon butter. Cover with aluminum foil and bake 30 minutes, then uncover and bake until golden, about 30 more minutes.