For the yeast dough, put the water in a bowl. Dissolve the yeast in it. Add salt and oil and stir. Add the flour and knead into a smooth dough with the dough hook of the mixer or the food processor. Divide the dough into 3 equal portions.
For the red dough, knead a portion of the dough with the tomato paste and a little flour until the dough is smooth again. For the green dough, knead the second portion of dough with the pesto and a little flour until the dough is smooth. For the white dough, knead the last portion of dough with the Parmesan and 2 tablespoons of oil. Cover and leave the three dough portions to rest for 20-30 minutes.
Divide each of the three dough portions into 8 equal pieces. You get a total of 24 parts. Shape each into an approx. 20 cm long roll. Make a braid from a red, a green and a white roll and place on a baking sheet lined with baking paper. Repeat this with all rolls until 8 braids are done. Cover and let rise in a warm place for about 30 minutes.
In the meantime, preheat the oven to 200 ° C top / bottom heat. If you like, you can brush the braids with a little oil before baking. Bake the braids for about 20 minutes.