Preheat the oven to 350ºF (175ºC). Line a rimmed baking sheet with parchment paper then add the walnuts in a single layer. Bake until the nuts are a few shades darker and you can smell the aroma of toasted nuts, 10 to 15 minutes. Let cool, then chop the walnuts into smaller pieces. Set aside.
In a medium saucepan, combine the cranberries, maple-flavored syrup, ginger, orange extract, cinnamon stick, clove, 1/2 teaspoon salt, and 1/2 cup water. Bring to a simmer over medium-high heat and cook until the berries begin to break open, 5 to 6 minutes. Keep cooking, stirring often, until berries are soft, about 10 minutes more.
Remove the saucepan from the heat and let the cranberry sauce cool and thicken for 5 minutes. Discard the cinnamon stick, stir in the chopped walnuts, then let the sauce cool to room temperature.
Transfer the sauce to a serving bowl, then cover it with plastic wrap, pushing the wrap onto the surface of the sauce. Refrigerate and let thicken until ready to serve.