Hydrate shallots with hot water in a small bowl, 5 to 10 minutes.
Drain.
Sift flour, baking powder, salt, cinnamon, and nutmeg together in a large bowl.
Whisk eggs, squash, shallots, and vanilla extract together in a separate bowl; stir into flour mixture until just mixed. Fold currants into batter.
Heat vegetable oil in a skillet over medium heat. Scoop about 1/4 cup batter and drop into hot oil. Cook pancakes until crisp and lightly browned, 6 to 8 minutes per side. Repeat with remaining batter.
Mix sour cream, vanilla extract, and maple syrup together in a bowl.