Cook rice according to package directions, using 1 teaspoon salt. Cool completely.
Cook sausage in a skillet over medium heat, stirring until it crumbles and is no longer pink; drain well. Let cool.
Stir together rice, sausage, black beans, and next 4 ingredients in a large bowl. Spoon about 1/3 cup rice mixture in center of each egg roll wrapper. Fold top corner of wrapper over filling, tucking tip of corner under filling; fold left and right corners over filling. Lightly brush remaining corner with egg; tightly roll filled end toward the remaining corner, and gently press to seal.
Pour oil into heavy Dutch oven; heat to 375º. Fry egg rolls, in batches, 2 to 3 minutes or until golden. Drain on wire rack over paper towels. Serve with Creamy Cilantro Dipping Sauce. Garnish, if desired.