Heat milk and water until warm (100ºF to 110ºF) in a small saucepan. Add yeast and allow to rest 5 minutes.
Combine 1-1/2 cups flour, 3 tablespoons sugar, salt, lemon peel and nutmeg in a large mixer bowl. Add 3 tablespoons butter, egg and yeast mixture. Beat until combined. Add enough remaining flour to make a soft dough.
Knead dough on lightly floured surface for 6 to 8 minutes, until dough is smooth and elastic. Shape dough into ball and place in greased bowl, turning once to coat. Cover and let rise until doubled in size; about 45 minutes.
Punch dough down. Roll dough into a 10 x 5-inch rectangle on lightly floured surface. Cut doughnut shapes with floured doughnut cutter. Reroll dough as needed, first letting dough rest for a few minutes. Place on greased baking sheet. Cover and let rise until doubled in size, about 30 minutes.
Dunk doughnuts in melted butter and return to baking sheet. Bake for 10 to 15 minutes in preheated 375ºF oven, or until lightly browned. Remove from baking sheet and cool slightly on wire rack.
Mix together sugar and cinnamon. Dip top half of doughnuts in remaining melted butter. Coat doughnuts with sugar mixture and serve warm.