Butter a 9x13-inch baking pan. Cut the bread into 1-inch cubes and spread them on a baking sheet to dry at room temperature while you prepare the other ingredients.
In a large skillet over medium heat, cook the bacon until crisp, about 15 minutes. With a slotted spoon, transfer the bacon to a plate lined with paper towels. Pour off all but 2 Tbs. of the fat from the skillet; reserve the extra. Put the onion in the pan and sauté over medium-high heat until soft and lightly browned, about 5 minutes. Sprinkle the sugar over the onion and sauté, stirring constantly to prevent sticking or burning, until the onion turns deep golden and the edges caramelize, 3 to 5 minutes. Scrape the onion into a large mixing bowl.
Return the pan to medium heat and add 2 Tbs. of the reserved bacon fat. Add the apples and celery. Sauté until softened, 5 to 7 minutes. Add the parsley, thyme, sage, 1/2 teaspoons kosher salt, and a few grinds of pepper; sauté another 1 minute. Scrape the contents of the pan into the bowl with the onion.
When you're ready to bake the stuffing, add the bread cubes and bacon to the bowl of sautéed vegetables and toss. Add the beaten eggs, broth, 1/2 teaspoons kosher salt, and a few more grinds of pepper; mix well. Transfer to the prepared baking pan.
Bake uncovered at 350°F until the top is light and crusty, about 1 hour.