Cut or tear the low-carb bread into small, 1/2"-1" cubes. Spread them out evenly on a baking sheet and toast in a 300°F (150°C) oven for 10–15 minutes, or until they feel dry and lightly crisp. Set aside to cool. 

In a large skillet over medium heat, cook the sausage until browned, breaking it into crumbles with a spatula. Once fully cooked, transfer the sausage to a large bowl, leaving the drippings in the pan.

Add the butter to the same skillet. When melted, add the diced shallot, garlic, and celery. Cook for 6–8 minutes, stirring occasionally, until the vegetables are softened and fragrant. 

Add the toasted bread cubes to the large mixing bowl that contains the cooked sausage, and pour the sautéed vegetables (with any butter remaining in the skillet) over the mixture. Toss gently to combine.

In a separate small bowl, whisk together the broth, egg, heavy cream, sage, thyme, salt, and black pepper until smooth.

Pour the custard mixture evenly over the bread and sausage. Gently fold together until all of the bread is moistened. Let the mixture sit for 5 minutes so the liquid can absorb.

Transfer the stuffing mixture into a greased 8x8 baking dish or similarly sized casserole dish. Cover with foil and bake at 350°F (175°C) for 20 minutes. Remove the foil, gently stir the stuffing, and bake uncovered for another 15–20 minutes, or until the top is golden and the center is set.