Sprinkle a half baking sheet lightly with a tablespoon of flour.
To the sponge add the remaining yeast, the milk and the eggs and with the paddle attachment mix on low speed until combined. With the mixer still on low speed add the remaining flour 1 cup at a time and continue to mix until all the ingredients all mixed together.
Switch to the dough hook, start on low speed and add the butter in 3 pieces waiting until 1 piece is mixed in before adding the next piece. When all the butter is added, increase the speed to medium and knead the dough until it pulls away from the sides of the bowl. This will take about 8 minutes.
After 8 minutes the dough should be smooth, elastic, and slightly sticky. Another way to check that it's ready is to gently stretch the dough until it is almost transparent. You should be able to do this without the tearing the dough. If the dough easily tears knead it with the mixer for 1 more minute.
Scrape the dough onto a a clean surface (without flour). Knead the dough for about 30 seconds until you have a smooth ball. Place the dough onto the baking sheet. Lightly dust the top of the dough with flour and cover with tea towel. Let the dough proof for 45-60 minutes or until the dough is doubled in size.
While the dough is rising, line two half baking sheets with parchment paper and lightly spray them with non-stick spray.
When the dough has risen gently turn the dough onto a floured surface. Divide the dough into about 15 pieces, 80 grams each. Roll each piece into smooth ball. Place the doughnuts on the baking trays about 3-inches apart.
Cover the doughnuts with tea towels Let them rise until doubled in height, about 45-60 minutes. If your kitchen is warm it might take less time.
While the doughnuts are proofing, fill a 5-quart pot with vegetable oil to a depth of 1-1/2-inches. Begin to heat the oil on medium low heat. The oil temperature will slowly rise. Use a candy thermometer or instant read thermometer to keep track of the temperature. Place a baking sheet with a cooling rack next to your cooking pot.
When the doughnuts are ready place them near the pot and increase the heat to medium-high heat and heat the oil to 360°F.
Cut the parchment paper into individual squares so each doughnut is on its own piece of parchment. Use the parchment squares to place the doughnuts into the hot oil and immediately remove the parchment squares from the oil.
Place 2-3 doughnuts in the pot and fry for one minute on each side. Use a set of chop sticks to turn the doughnuts over and a spider skimmer to remove the doughnuts from the pot and place them on the rack.
As the doughnuts fry you will need to adjust the temperature on your stove to keep the oil from getting too hot or too cool. If the oil gets too hot (above 370°F), remove the pot from the heat and allow to cool. On my stove I am able to maintain temperature at medium low heat.
When the doughnuts are cool enough to handle, but still warm roll them in the strawberry sugar dust.
Let them cool before filling with the strawberry mascarpone filling.