Preheat the oven to 375 degrees F and butter a 3-quart baking dish. Melt 8 tablespoons (1 stick) butter in a large pot or Dutch oven over medium-high heat. Add the celery, leeks, apples, chestnuts, thyme, sage, 1 teaspoon salt and a few grinds of pepper. Cook, stirring occasionally, until the vegetables are tender, about 5 minutes. Add the chicken broth and bring to a simmer, then remove from the heat and set aside.
Whisk the eggs and 3 tablespoons parsley in a large bowl. Add the bread cubes, dried cherries and the vegetable mixture; stir to combine. Transfer the stuffing to the prepared baking dish. Cut the remaining 2 tablespoons butter into cubes and dot over the stuffing. Cover with foil and bake 30 minutes, then uncover and bake until golden brown, about 20 more minutes. Sprinkle with the remaining 1 tablespoon