Let bread cubes dry overnight, uncovered, on the counter. (Or, bake at 300 F for 12 to 14 minutes). Place bread cubes in to a large bowl.

Preheat oven to 350 F.

Cook sausage in a large skillet over medium-high until browned, about 6 minutes, using a spoon to break sausage into small pieces. Transfer sausage to bowl with bread cubes. (Do not wipe skillet clean.) Reduce heat to medium. Add butter, onion, and celery to skillet; cook, stirring occasionally, until vegetables are tender and translucent, 6 to 8 minutes. Add apples; cook until soft but not mushy, about 10 minutes. Stir in sage, thyme, salt, and pepper; cook, stirring constantly, until fragrant, about 1 minute. Add 1 cup stock, stirring and scraping bottom of skillet to release browned bits. Transfer apple mixture to bowl with bread cubes and sausage.

Whisk together eggs and remaining 1/2 cup stock in a bowl until combined; stir into bread mixture. Transfer mixture to a 2-quart glass or ceramic baking dish, cover with aluminum foil, and bake at 350°F for 15 minutes. Remove foil, top with thyme sprigs, and continue to bake until stuffing is lightly browned on top and set, 15 to 20 more minutes. Let stuffing stand 5 minutes before serving.