Dissolve the yeast in the water and mix it with the flour, salt, and oil until it forms a smooth dough. Cover it and allow it to rise for 30 minutes.
In the meantime, clean the carrots, peel them, and cut them into thin slices. Peel the onions and cut them into slices, as well. Peel the garlic and dice it. Put some thyme aside for a garnish and chop the rest.
Mix garlic, carrots, onions, and chopped thyme with 2 tbsp oil and season it with salt and pepper.
Heat the oven to 250°C / 480°F (fan: 230°C / 445°F).
Roll out the dough and coat it with sour cream. Distribute the carrot mix evenly on the pizza and sprinkle the grated cheese on top. Bake it in the preheated oven for approx. 20 minutes. Garnish with the thyme and freshly ground pepper.