Stir 2¼ teaspoons of active dry yeast into a little of ¾ cup of lukewarm water with a pinch of ¼ cup of sugar, and leave for about 10 minutes, until foamy.
Whisk in the remaining water and sugar, ¼ cup of canola oil, 2 large eggs, and ¾ teaspoon of vanilla extract.
Put 510g of all-purpose flour and 1 teaspoon of salt in a stand mixer. Add the liquid and mix on low for about 10 minutes, until a very sticky dough forms. Add 1 tablespoon of vodka and mix for 2-3 minutes more.
Cover and let rise in a warm place for about 2 hours, until doubled.
Roll out on a floured surface to ½in / 1cm thick. Cut out rounds with a floured cutter, rerolling the scraps. Dust with flour, cover, and let rise for about 45 minutes.
Toward the end of the rise, heat 6 cups of grapeseed oil in a deep pot to 325°F / 165°C. Fry up to 4 doughnuts at a time for about 90 seconds per side, until golden, keeping the oil at that temperature. Drain on paper towels.
Spoon 1¼ cups of smooth strawberry jam into a squeeze bottle. Poke a hole in each slightly cooled doughnut with a straw and squeeze in jam until it just overflows. Dust with ½ cup of icing sugar just before serving.
