Heat butter in a large saucepan over medium-high heat. When butter is melted and frothy add pears, tossing with a wooden spoon to coat. Add 1/4 cup of sugar, stirring to combine. Bring to a boil, then reduce heat to low. Add grated ginger and cook over low heat for about 15 minutes, until pears are soft and most of the liquid has evaporated. Remove from heat and allow to cool for at least 15-20 minutes. Put oven rack in middle position and preheat oven to 400°F. Grease muffin pan. Stir together flour, baking powder, baking soda, 1 teaspoon of ground ginger, and salt in a bowl. Whisk together eggs and 1/3 cup sugar in a large bowl until combined well, then add butter whisking or blending with electric mixer until creamy. Stir in pear ginger sauce, then fold in flour mixture to combine. Stir in 1 cup of walnuts and divide batter among muffin cups. In a small bowl, combine remaining 2 tablespoons sugar, 1/2 teaspoon ground ginger and 1/2 cup walnuts. Sprinkle topping evenly on top of muffins. Bake until muffins are golden and toothpick inserted into the center comes out clean, about 20 minutes. Cool in pan on a rack 5 minutes, then remove muffins from pan and cool slightly. Enjoy with coffee, preferably in a sunny spot in the backyard. Once cooled completely, the muffins can be stored in an airtight container at room temperature 1 day, or in the freezer for about a week.