Dissolve white sugar and yeast in warmed milk. Let stand until foamy, about 10 minutes.
Pierce yam in several places in a fork. Cook in the microwave until soft, about 7 minutes. Mash with a fork on a small plate.
Whisk egg and vanilla extract together in a small bowl.
Sift whole wheat flour, all-purpose flour, 1 teaspoon brown sugar, cinnamon, and salt together in a large bowl. Add milk mixture, mashed yam, and egg mixture; stir until batter is the consistency of sour cream.
Heat a large nonstick skillet over medium-high heat; grease with cooking spray. Drop 1/4 cup batter onto the skillet; cook until edges are dry, 30 to 40 seconds. Flip and cook until browned on the other side, about 30 seconds more. Transfer to a plate. Repeat with remaining batter, greasing skillet between batches.
Combine 1/2 cup milk, 3 tablespoons brown sugar, ginger, and cornstarch in a small saucepan. Cook over medium heat, whisking constantly, until smooth and thick, 3 to 5 minutes. Pour over blinis.
