To make the homemade noodles, crack the two eggs into a bowl, add the five tablespoons of sifted flour, then sprinkle in a pinch of salt.
Stir the mixture with a fork at first, then knead it by hand until you get a smooth, elastic dough, and let it rest for about 20 minutes.
Roll the dough out into a thin sheet, dust it generously with flour, then roll it up into a loose log. Sprinkle more flour to prevent sticking, slice the roll into thin strips, and set the noodles aside to dry slightly.
Chop the tomatoes, place them in a pot, and simmer them gently for about 5 minutes.
Strain the tomatoes through a fine sieve to remove the skins and seeds, pressing well until you obtain a thick, smooth tomato puree (about 4 cups).
Cut the chicken fillet into small cubes and sauté them in the olive oil. Add the finely chopped onion, cook for 5 minutes, then stir in the carrot matchsticks.
Season with salt, sugar, and herbs, then cover and cook over very low heat until the chicken is tender, adding a splash of water if needed. Once the meat and vegetables are soft, pour in the tomato puree and thin it with about ¾ cup water.
Bring the soup to a gentle boil, add the homemade noodles, and cook for about 5 minutes, then turn off the heat.
Finish the soup with a generous handful of fresh chopped herbs on top. Serve warm and enjoy!