Stir the ¼ cup of flour and 1/3 cup water together in a small pot. Place over a medium heat on the stove and cook until the mixture has thickened into a stiff paste. Remove from the heat and set aside to cool.
Make the dough:
In the bowl of a stand mixer, combine the yeast and lukewarm water. Let it stand for 10 minutes until bubbly. Add the cooled paste you made earlier, the flour, sugar, salt and vegetable oil to the bowl of the stand mixer. With the dough hook attached, knead the dough in the mixer for 6 minutes on a medium speed until smooth and elastic. Pour a little bit of oil into the bowl and turn the dough so that the oil coats the dough. Cover with a damp cloth and set aside in a warm place until doubled in volume, about 2 hours.
Once risen, punch the dough down and tip out onto a floured counter. Roll out to be 1/4-inch thick and use a 3-inch round cutter (or a glass that width) to punch out circles from the dough. Use a pastry tip to cut out the centre of each circle to make the doughnut hole. Place onto a floured baking tray and cover with a damp tea towel, leave in a warm place for 30 minutes to rise.
Heat ½-inch depth of vegetable oil in a deep frying pan to 350oF. Gently lower in a few dougnuts into the oil. Let fry until golden underneath then flip and let it cook until the other side is golden. Remove to a baking tray lined with kitchen paper.
For the glaze, stir together the powdered sugar, vanilla extract and soy cream in a medium bowl until you get a thick but drizzleable glaze. Divide between 4 small bowls. Leave one white. Colour one a very pale blue. Colour one a dark blue/purple. Colour another pink. Dollop a few dots of the dark blue and pink glaze into the light blue glaze. Swirl a few times with a spoon just to lightly combine then drizzle in some of the white glaze. Using a swooshing motion, dip a doughnut into the glaze and place glaze-side up on a wire rack to set. Repeat with the remaining doughnuts adding more of the dark blue/pink/white glaze to the bowl as needed. Decorate with a few sprinkles or edible glitter if you’d like for extra flair.