Heat the oil in a large pot and sauté the onion, carrots, and bell pepper until softened.
Grate the tomatoes and add them to the pot.
Pour in the water and add the rice.
Bring to a boil, then simmer for 20 minutes.
Meanwhile, whisk the egg with the semolina and bicarbonate of soda.
Leave the mixture to rest for 10 minutes.
Bring a separate pot of water to a boil.
Spoon small portions of the dumpling mixture into the boiling water.
Cook the dumplings for about 15 minutes.
Transfer the cooked dumplings into the soup using a slotted spoon.
Season with salt and simmer for another 10 minutes.
Stir in the chopped dill and serve hot or cold.