Generously butter a (or spray with non-stick spray) 12 large or 16 medium muffins pan.
Combine chopped cranberries with 1/2 cup sugar.
Whisk or sift together (sifting will make for lighter muffins), flour, baking powder, salt, and 3 tablespoons sugar. Beat egg, add milk and beat well. Add melted butter or shortening. Stir quickly into dry ingredients, mixing well just until dry ingredients are moistened, some lumps will remain.
Stir in cranberries, chopped nuts, and orange peel (optional).
Bake at 400°F for 20 or 25 minutes.
Remove from oven; brush muffin tops with melted butter. Sprinkle with coarse sugar or cinnamon sugar, if desired.