Stir the apple cider, brown sugar, ginger, nutmeg, and salt together in a small container.
Melt the butter in a large skillet over medium heat. Push the butter around to evenly coat the bottom of the skillet, then add the tofu slices in an even layer. Cook the tofu for about eight minutes, flipping the pieces halfway through, until they're golden brown on both sides. Transfer the tofu to a plate when done.
Turn up the heat to medium-high. You can add a bit more butter to the skillet at this point if it seems dry. Add the shallot and sauté it for about five minutes, until soft and just beginning to brown.
Push the shallot to the side and add the minced garlic to the skillet. Sauté the garlic for about one minute, stirring constantly, until it becomes very fragrant.
Add the apple, rosemary sprig, and the apple cider mixture to the skillet. Raise the heat and bring the liquid to a boil, then lower the heat and let everything cook at a low simmer. Gently stir everything occasionally. Let the mixture simmer for about ten minutes, until the liquid reduces by about half.
While the mixture simmers, stir the cornstarch and cold water together in a small container. Add the cornstarch mixture to the skillet, give the mixture a quick stir, then return the tofu to the skillet. Bring the liquid back to a simmer. It should thicken slightly. Once this occurs, you can remove it from heat.
Remove the rosemary sprig from the skillet, then season the tofu with additional salt to taste, along with some black pepper.
Serve.