Preheat The Oven To 375F. Grease the muffin tins. Cut the unpeeled ginger until it is in tiny pieces; or hand chop into fine pieces. (You should have 1/4 cup; it is better to have too much ginger than too little.) Put the ginger and 1/4 cup sugar in a small skillet or pan and cook over medium heat until the sugar has melted and the mixture is hot. Don't walk away from the pan-this cooking takes only a couple of minutes. Remove from the stove and let the ginger mixture cool. Put the lemon zest and 3 tablespoons sugar in the food processor and process until the lemon peel is in small bits; or chop the lemon zest and pith by hand and then add the sugar. Add the lemon mixture to the ginger mixture. Stir and set aside. Put the butter in a mixing bowl and beat a second or two, add the remaining 1/2 cup sugar, and beat until smooth. Add the eggs and beat well. Add the buttermilk and mix until blended. Add the flour, salt and baking soda. Beat until smooth. Add the ginger-lemon mixture and mix well. Spoon the batter into the muffin tins so that each cup is 3/4 full. Bake 15 to 20 minutes. Serve warm.
