Preheat oven to 350°F. Butter or line with paper liners, 18 (2½-inch) muffin cups.
Peel ginger root. Cut into chunks (about ⅔ cup) and process in a food processor with metal blade, until finely minced. (Or grate or mince ginger by hand.) Melt butter, combine with ginger and set aside.
Whisk together flour, sugar, baking soda and salt in a bowl, create a well in the center of the mixture, and then set this mixture aside.
Whisk together buttermilk, eggs, and ginger/butter mixture. Add wet ingredients all at once to well in dry ingredients. Stir just until dry ingredients are moistened; do not over mix. Spoon batter into 18 prepared muffin cups. Sprinkle with chopped nuts.
Bake 25 minutes at 350°F or until tops are browned and a wooden toothpick inserted in a muffin comes out clean. Serve muffins warm with Lemon Butter.
Combine butter with powdered sugar and lemon zest; beat until creamy. Gradually beat in lemon juice. Cover and refrigerate until ready to serve.