Heat up milk in the microwave. Add vanilla sugar, and yeast. Mix to combine, let sit for yeast to activate.
In a bowl, combine sugar, grapeseed oil, eggs, rum, lemon extract, and a pinch of salt.
Put half of the flour in a KitchenAid bowl with a hook attachment. Add the wet ingredients (including the milk yeast mixture), and combine. Add the rest of the flour and knead until the dough is smooth.
Let the dough rest in an oiled bowl until doubled in size.
In the meantime, cut 16 squares of parchment paper. Brush them with oil, and arrange on a baking sheet.
Remove the dough from the bowl, punch down, and roll out. Using a round circle cutter (2 1/4″), cut about 16 donuts.
Place the donuts on the paper squares, and let rise again (covered).
Heat up oil to 320F. With your fingers, transfer each square onto a spatula and carefully drop it into the oil. Use thongs to remove the parchment paper and place aside.
Fry the donuts – about 2 minutes on each side. Transfer donuts to a bowl lined with paper towels. Once cooled a little bit, cut midway and spread strawberry jam. Sprinkle icing sugar and serve right away.