Combine water, rice, carrot, peas and salt in a saucepan. Bring to the boil; reduce heat and simmer until rice is tender but still firm to the bite, about 14 minutes. Drain excess water; let cool, 10 to 15 minutes.
Mix prosciutto cotto, cheese, button mushrooms, sweetcorn, green olives, black olives, pickle, artichoke hearts, olive oil, thyme and oregano together in a large bowl. Stir in cooled rice mixture. Fold tuna into the salad.
Divide salad among 4 serving plates; garnish with hard-boiled eggs. Chill before serving, at least 30 minutes.