Preheat the oven to 375 degrees F and line a baking sheet with parchment paper. Arrange the sausages on the baking sheet and bake until lightly browned and cooked through, about 10 minutes. Remove from the oven and set aside; reduce the oven temperature to 200 degrees F.
Meanwhile, whisk the eggs, milk, granulated sugar, cinnamon, nutmeg and salt in a large bowl. Trim each slice of bread into a 2-by-4-inch rectangle, then flatten slightly with your fingertips. Starting at a short end, roll each piece of bread around a sausage, pressing firmly to seal. Transfer to the bowl with the egg mixture and soak 5 minutes.
Melt 2 tablespoons butter in a large nonstick skillet over medium heat. When it begins to brown and foam, add 6 of the bread-wrapped sausages and cook, turning occasionally, until golden brown, about 5 minutes. Remove to a paper towel-lined baking sheet and keep warm in the oven. Wipe out the skillet, add the remaining 2 tablespoons butter and repeat with the remaining 6 sausages. Dust with confectioners' sugar and serve with maple syrup.