Preheat the oven to 350°F.
Line an 8 x 4 inch loaf pan with parchment paper and lightly grease it. In a large mixing bowl, combine the almond flour, coconut flour, baking soda, and sea salt. In a separate bowl, whisk together the eggs, melted butter, almond milk, and apple cider vinegar. Pour the wet mixture into the dry ingredients and stir until thoroughly combined.
Transfer the batter to the prepared loaf pan and smooth the top.
Bake for 30 to 35 minutes, or until the bread is golden and a toothpick inserted into the center comes out clean.
Allow the bread to cool completely before cutting it into approximately 1-inch cubes.
Spread the bread cubes across a large baking sheet. Bake at 300°F for 20 to 30 minutes, stirring halfway through, until the cubes are dry and lightly toasted. Set aside to cool.
Increase the oven temperature to 375°F. Lightly grease a 9 x 13 inch baking dish.
Melt the butter in a large skillet over medium heat. Add the onion and celery. Cook for 7 to 9 minutes, stirring occasionally, until softened.
Add the garlic, sage, rosemary, thyme, sea salt, and black pepper. Cook for another 1 to 2 minutes, until fragrant.
Place the toasted grain-free bread cubes in a large mixing bowl. Add the cooked vegetable and herb mixture and gently toss to combine.
Pour 1 1/2 cups of broth over the mixture and gently toss. Add more broth a little at a time if needed. The bread should be evenly moistened but not soggy.
Add the beaten eggs and fresh parsley. Gently fold everything together until evenly combined. Transfer the stuffing mixture to the prepared baking dish and spread it into an even layer.
Cover the baking dish with foil and bake for 20 minutes.
Remove the foil and continue baking for 15 to 20 minutes, until the top and edges are golden and crisp.
Allow the stuffing to rest for 5 to 10 minutes before serving.