Preheat oven to 350 degrees F.

Spray 6 giant (1 1/4 cup) muffin cups or 18 standard (1/3 cup) muffin cups with nonstick spray.

Sift flour, ginger, baking soda, and salt into a medium bowl.

Using an electric mixer, beat 1 cup sugar and oil in a large bowl to blend.

Beat in eggs one at a time, blending well after each addition.

Beat in pumpkin, 1/2 cup molasses, buttermilk, and 1/4 cup crystallized ginger.

Stir in flour mixture until well blended.

Divide batter among prepared muffin cups.

Bake muffins until a tester inserted into the center comes out clean, about 40 minutes for giant muffins and 30 minutes for standard muffins.

Transfer muffins to a rack to cool completely.

Whisk powdered sugar, 1 1/2 tablespoons water, and remaining 1 tablespoon molasses in a medium bowl, adding more water as needed to form a thick glaze.

Dip muffin tops in glaze.

Transfer to a rack, allowing glaze to drip down sides.

Sprinkle with remaining 1/4 cup crystallized ginger.

Let stand until glaze is set, about 1 hour.