Preheat the oven to 375 degrees. Lightly butter a 9-by-13-inch baking dish. On a large rimmed baking sheet, toast the rye bread cubes for about 15 minutes, tossing once halfway through, until lightly golden and dry. Transfer the bread to a large bowl.

In a skillet, melt the butter. Add the onion and celery; cook over moderate heat until tender, about 10 minutes. Add the sage and thyme and cook until fragrant, about 1 minute. Scrape into the bowl with the bread.

Wipe out the skillet. Add the bacon and cook over moderate heat until browned, about 10 minutes. Using a slotted spoon, transfer the bacon to the bowl with the bread. In a medium bowl, whisk the chicken broth with the egg. Pour over the bread mixture and add the kosher salt and pepper. Toss until the bread soaks up the liquid. Scrape into the prepared baking dish and cover with foil. Refrigerate for at least 1 hour or overnight.

Bake the stuffing for about 30 minutes, until hot throughout. Remove the foil and bake for about 30 minutes longer, until the top is lightly golden. Serve hot or warm.