Preheat oven to 400 degrees. Line two baking sheets with parchment paper or a nonstick baking mat; set aside.
In a large bowl, toss celery root with vegetable oil and 1 teaspoon salt. Evenly spread celery root on one of the prepared baking sheets. Transfer to oven and roast until just cooked through, about 40 minutes (celery root should still be slightly crisp). Remove from oven and set aside.
In a large bowl, toss bread cubes with 1/4 cup olive oil. Evenly spread bread cubes on second prepared baking sheet; season with salt and pepper. Transfer to oven and bake until golden and slightly crunchy, about 20 minutes. Remove from oven and let cool slightly.
Cut Swiss chard leaves into 1-inch-wide strips and finely chop stems. Heat a large skillet over medium heat. Add remaining 1/4 cup olive oil, garlic, Swiss chard stems, and red-pepper flakes. Cook, stirring, until soft and translucent, about 5 minutes. Add leaves and 1/4 cup mushroom stock. Cover and cook until leaves are soft, but not mushy, adding a tablespoon mushroom stock as necessary, about 10 minutes. Season with salt and pepper and set aside.
Coat two nonstick 9-by-5-by-2 3/4-inch loaf pans with olive oil; set aside.
In a large bowl, whisk together eggs, remaining 1 1/2 cups mushroom stock, 2 teaspoons salt, and 1 teaspoon black pepper. Add celery root and bread cubes along with persimmons, raisins, almonds, and parsley; mix until just coated.
Divide one third of the bread mixture evenly between each prepared loaf pan. Top each with one quarter of the Swiss chard mixture. Repeat process and top with remaining third of bread mixture, evenly divided. Cover loaf pans with parchment paper-lined aluminum foil. Transfer to oven and bake for 50 minutes. Uncover, and continue baking until top is golden brown, about 10 minutes.
Remove from oven and let cool to room temperature. Carefully unmold onto a platter. Garnish with persimmon slices and fresh herbs; serve.