Gingerbread Waffles with Caramelized Squash

Name: Gingerbread Waffles with Caramelized Squash
Ingredients: 1 tablespoon vegan butter, preferably unsalted, plus 4 tablespoons at room temperature, divided; 1 small butternut squash, peeled, seeded and cut into 1/4-inch cubes; Water as needed; 3 tablespoons brown sugar, divided; 1 tablespoon confectioners’ sugar; 2 ⅛ teaspoons ground cinnamon, divided; ¾ cup all-purpose flour; ¾ cup whole-wheat flour; 1 tablespoon baking powder; ½ teaspoon salt; 1 ¼ cups unsweetened soymilk; ¼ cup canola oil; 1 tablespoon grated fresh ginger; 2 teaspoons molasses; 2 teaspoons vanilla extract; Maple syrup for serving