Mix together yeast, water, and sugar in a large bowl.
Add salt, oil, and half of the flour.
Work the dough together and add the rest of the flour little by little.
Knead the dough at medium speed for about 5 - 6 minutes (or about 10 minutes by hand) until the dough is glossy, smooth, and elastic.
Remove the dough from the bowl, grease a glass bowl with a little oil, put the dough in the glass bowl, and grease the dough as well.
Cover the glass bowl with plastic wrap and a kitchen towel and allow the dough to rise at room temperature until it doubles in size.
Roll the dough into a thick log shape and roll it out into a rectangle. Spread the loaf with pesto and sprinkle over the vegan crumbled feta cheese
Roll the loaf tightly together like a roll cake and divide it into 12 equal pieces.
Place the spinners next to each other in a baking pan. There should be some air between the spinners (but no more than that they grow a little together during raising). Cover with plastic wrap and leave the spinners to rise for about 30 minutes.
Brush the spinners with the mayo/ketchup/soy milk and bake the spins in the middle of the oven at 180°C / 350°F, for about 30 minutes.