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 a lightly floured surface for 6 to 8 minutes, until dough is smooth and elastic. Shape dough into ball and place in a 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 a lightly floured surface. Cut doughnut shapes with floured doughnut cutter. Reroll dough as needed, first letting the 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 the baking sheet. Bake for 10 to 15 minutes in preheated 375ºF oven, or until lightly browned. Remove from the baking sheet and cool slightly on a wire rack.
Beat butter at the medium-low speed of an electric mixer until smooth and creamy (1 to 2 minutes.)
Gradually add 6 cups powdered sugar, vanilla bean seeds, and vanilla extract with a mixer at low speed, scraping the bowl occasionally. Mix until blended.
Beat at medium-high speed for 3 to 5 minutes, until buttercream is light and airy and nearly white. If needed, add the additional powdered sugar or milk until desired consistency.
Add food colouring a few drops at a time, if desired. Mix well until the desired colour is achieved.
Using a spatula, spread the frosting on top of the doughnuts. Sprinkle with crushed chocolate eggs.