• To make the starter, whisk together the yeast, flour, sugar, and milk in a large measuring cup. The mixture will be lumpy. Rest for 1 hour, or until it's frothy and doubled in size.

For the donuts:

• Place the eggs and sugar in the bowl of an electric mixer fitted with the whisk attachment and whisk until frothy. Add the vanilla, lemon juice, and salt and whisk. Switch to the paddle attachment.
• Add the starter and 3 Tablespoons of the flour and beat until smooth.
• Add the rest of the flour in about 1/2 cup increments, beating well after each addition. The dough is ready when it begins to pull away from the sides of the bowl and is tacky, but not super wet. Add the butter at the very end and beat until just combined.
• Transfer the dough to a lightly floured surface and knead for about 1 minute, or until the dough smooths out.
• Place the dough in a lightly oiled bowl and cover with plastic wrap. Set in a warm place to rise for 45 minutes to 1 hour.
• Line a large baking sheet with parchment paper. Grab about a 1/4 cup portion of dough and roll it into a ball in your hands. Repeat with remaining dough. Alternatively, roll the dough to about 3/4 inch thick, then cut rounds with a biscuit cutter. Cover the dough balls and allow to rest for 30 minutes.
• Heat 4-5 inches of oil in a heavy bottomed pot to 345-660 degrees. Use a slotted spoon to lower the dough into the hot oil 4-5 at a time and fry for 2-3 minutes each side, or until golden brown. (It can be helpful to start with a test donut to make sure the oil isn't too hot or cold and see how long it takes for them to cook clear through.) Use tongs to remove the donuts and place them on a paper towel lined plate.
• Fill a shallow bowl with granulated sugar and roll the donuts in the sugar while still warm. (If using powdered sugar only, skip this step).
• When the donuts are cool enough to touch, use a chopstick to poke a small hole about 3/4 of the way through the donut. I like to twist it around slightly to make sure there is enough space for the filling. Fill a piping bag with strawberry jam, insert the tip into the donut and squeeze until the jam starts to pool at the top. Repeat with remaining donuts.
• Sift powdered sugar over top of the donuts. Serve warm or store in an airtight container for up to 3 days.