Adjust oven rack to center position and heat oven to 425 degrees. Spray 24 mini muffin cups with vegetable cooking spray.
Place pumpkin, ginger, cinnamon, and cloves in a small nonstick skillet over medium heat. Bring to a simmer and cook, stirring, to blend flavors, about 3 minutes. Pour hot puree into a medium bowl. Whisk in brown sugar and oil, then slowly beat in eggs.
Whisk flour, cornstarch, baking powder, baking soda, and salt in a medium bowl. Whisk pumpkin mixture into flour mixture until just combined.
Divide batter among muffin cups (a 2-tablespoon spring-action ice cream scoop works well) and bake until golden and cooked through, 10 to 12 minutes. Let muffins stand for a couple of minutes, then remove from the cups and place on a wire rack to cool.
ORANGE GLAZE (OPTIONAL):
Whisk ingredients together in a small bowl. Drizzle over warm muffins.