In a heavy saucepan, simmer milk, rice, sugar, salt and 1/2 cup half-and-half, covered, until rice is tender and most liquid is absorbed, about 30 minutes.
While rice is cooking, in a small saucepan simmer jelly, water, cranberries or raisins, and lemon juice, covered, stirring occasionally, until jelly melts and sauce thickens slightly. Keep sauce warm.
In a measuring cup, beat together with a fork egg, vanilla and remaining 1/4 cup half-and-half.
Remove rice from heat and stir in egg mixture. Cook rice pudding over low heat, stirring constantly, until thick and creamy, about 5 minutes.
Stir walnuts into sauce and serve rice pudding with sauce.
