Rinse rice, add 2 cups of cold water, put on high heat and bring to a boil. Reduce heat, boil until tender. Grind the rice in a blender, or rub it through a sieve.
Wash the zucchini, peel and cut into large cubes; plunge into boiling salted water for 2 minutes. Drain in a colander, then grind in a blender. Mix mashed rice with zucchini puree in a saucepan, add milk and butter, put on fire and bring to a boil. Salt to taste. Add sugar if desired.
Peel carrots, cut into thin strips. Fry in hot vegetable oil until crispy. Add to soup.