Wash the potatoes thoroughly and place them in a pot. Cover with water and bring to a boil. Boil the potatoes for about 20 minutes until soft.
Let the potatoes cool down a little. Then peel and mash them with a potato masher.
Add salt and flour a little at a time and quickly knead into a smooth dough.
Dust a clean working surface with flour and roll out the dough with a rolling pin to a rectangle about 2cm (¾ inch) thick, dusting the rolling pin if necessary.
Then cut 2cm (¾ inch) wide strips and roll up with your hands.
Cut 2 cm (¾ inch) long pieces with a knife.
Place gnocchi on a clean kitchen towel and let dry for 30 minutes.
In the meantime, prepare the sauce. Put the tomatoes together with the basil, a pinch of salt and a generous dash of olive oil in a cast iron pan or casserole dish. Bake for 30 minutes at 200 °C (392 °F). Then put cooked tomatoes and sour cream in a blender, puree with salt and pepper and set aside.
Cook gnocchi in boiling salted water until they float to the surface, then drain and serve immediately with the sauce.