Melt butter in milk in a microwave safe bowl on high in a microwave for 1 minute. Set aside.
Combine flour, yeast, salt and sugar in a bowl.
Beat the egg into the milk mixture then pour over the dry ingredients and mix.
When combined, knead by hand for 10 minutes until soft and silky. Add a little more flour if needed.
Place in an oiled mixing bowl, cover and keep in a warm spot for 1 hour or until doubled in size.
Punch the dough down and knead again, cut in half and roll out two long 30 cm sausages then cut into eight slices, finally roll into little balls. Place each ball onto a tray and allow resting for 20 minutes.
Heat oil in a deep heavy based saucepan to 180C or deep fryer, carefully place doughnuts into the oil, cooking 4 - 6 at a time, turning with a spatula so they become evenly golden and puffed (2 – 3 mins).
Drain on absorbent paper towel, then roll in sugar and pipe a teaspoon of apricot jam into half the doughnuts and Nutella into the other half.