Mix all the ingredients for the dough and knead it thoroughly for about 10 minutes. Form a ball out of the dough, cover it with a cloth and let it rise at a warm place for 2-3 hours.
Place all the ingredients for the herb pesto in a blender and blend thoroughly. Stop the blender at least twice and push the leftovers on the side of the blender down to mix everything well. Place the pesto in a bowl and repeat the process with the dried tomato pesto. If you only want to make one of the two pestos, just double the amount.
Knead the dough only briefly after the resting period and cut it in two parts. Roll one half into a 40 x 30cm rectangle and spread a pesto over the dough. Fold one half of the rectangle onto the other, so that the shorter sides are on top of each other and a smaller rectangle is created.
Preheat the oven to 200 degrees Celsius or 356 degrees Fahrenheit.
Now cut down strips of 2cm thickness along the shorter side of the dough. Take a strip and twist it a few times, then you can roll it into a roll. Place the roll on a baking tray with baking paper and repeat the process with all the strips and then with the other half of the dough and the other pesto.
Bake the pesto buns in the oven for about 17-20 minutes and serve while still warm.