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 tester inserted into center comes out clean, about 40 minutes for giant muffins and 30 minutes for standard muffins. Transfer muffins to rack; cool completely.
Whisk powdered sugar, 1 1/2 tablespoons water and remaining 1 tablespoons molasses in a medium bowl, adding more water as needed to form thick glaze. Dip muffin tops in glaze; transfer to rack, allowing glaze to drip down sides. Sprinkle with remaining 1/4 cup crystallized ginger. Let stand until glaze is set, about 1 hour.