Put the bread on a rack and dry on the counter overnight. Alternatively, dry the bread on a baking sheet in a 275°F oven, stirring occasionally, until crisp, 15 to 45 minutes.
Position a rack in the center of the oven and heat the oven to 350°F. Put the bread in a very large mixing bowl.
Heat 1/4 cup of the olive oil and 1/4 cup of the butter in a 12-inch skillet over medium-high heat. Add the onions, celery, leek, 1 tsp. salt, and 1/2 tsp. pepper. Cook, stirring often, until beginning to color, 10 to 15 minutes. Stir in the apples, reduce the heat to medium low, cover, and cook, stirring occasionally, until soft and lightly browned, 10 to 15 minutes more. Add the vegetables and fruit to the bread.
Heat the remaining 1 Tbs. olive oil in the skillet over medium heat. Add the garlic and cook, stirring, until fragrant, about 30 seconds. Add the mushrooms and a big pinch of salt. Cook, stirring often, until golden-brown, 5 to 6 minutes. Add the mushrooms to the bread mixture, along with the walnuts, cherries, prunes, and all of the herbs. With your hands, gently but thoroughly toss.
Pour 1-1/2 cups of the vegetable broth over the mixture and thoroughly mix again. If the liquid is immediately absorbed, add another 1/2 to 1 cup broth. If a little liquid pools at the bottom of the bowl, you’ve added enough. Continue tossing occasionally until the liquid is fully absorbed. Season to taste with salt and pepper. Stir in the eggs.
Transfer the stuffing to a large (roughly 11x13-inch) oiled baking dish. Bake until hot throughout, 40 minutes if starting at room temperature or 50 minutes if refrigerated. Dot the top of the stuffing with the remaining 2 Tbs. butter and bake until the top is crisp, 5 to 10 minutes more.
The stuffing—minus the broth and eggs—can be refrigerated in an airtight container for up to two days before finishing and baking.