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in a small saucepan warm the milk with butter, until butter melts
remove from the heat, and stir in sugar and salt
allow to cool to slightly more than lukewarm (100- 110 degrees)
combine the yeast with 3 cups of flour
stir in milk and eggs
knead dough (either by hand on a well floured surface, or using the dough hook of a stand mixer) adding enough of the extra flour to create a smooth ball of dough (dough should not be sticky)
place the dough in a bowl, cover and let rise until doubled, about 90 minutes
on a floured surface, roll dough to 1/2 inch thickness
cut with a round cookie cutter (2 – 3 inches) or a biscuit cutter
place rounds on a floured baking sheet, cover and rise 30 – 45 minutes
while the rounds are rising, heat oil (about 3 inches deep) in a large deep pot to 375 degrees on a deep-fat thermometer
fry doughnuts (no more than 2 at a time) flip after 45 seconds,and cook until golden (1 1/2 – 2 minutes total)
drain doughnuts on paper towels
cool only until you can handle them comfortably,and then using a skewer poke a hole in the side of each doughnut
toss doughnuts in granulated sugar
place jam in a piping bag fitted with a round tip (I use a Wilton #12 – smaller tips tend to get clogged with the jam)
pipe jam into each doughnut
enjoy warm

doughnut recipe from epicurious jam recipe from ball