Preheat oven to 375°F.
Cream butter, ginger, salt and 1¼ cups sugar. Blend in molasses and egg. Combine flour, baking powder and baking soda; blend into the mix. Stir in minced ginger. (Chill dough slightly if desired for ease of handling and to reduce spread.)
Form dough into 1-inch balls and roll in sugar to coat, then arrange approximately 2-inches apart on a buttered baking sheet.
Bake 10 minutes. Let cool on the baking sheet for 2-3 minutes before transferring to racks to finish cooling. Store in an airtight container.