To prepare croquette mixture: In medium saucepot, heat potato, salt and enough cold water to cover to boiling over high heat. Reduce heat to low; simmer 4 minutes or until tender. Drain and rinse potato with cold water; drain and dry well.
In medium bowl, whisk egg; add cheese, ham, rosemary, pepper and potato. Toss to combine; cover and refrigerate 30 minutes.
To prepare croquette coating: In wide, shallow dish, whisk eggs and water; place breadcrumbs in second wide, shallow dish; place flour in third wide, shallow dish.
To prepare dipping sauce: In small bowl, whisk garlic, mayonnaise, mustard and pepper; fold in green onions. Cover and refrigerate until ready to serve. Makes about 1 cup.
Form 2 tablespoons croquette mixture into 1x2-inch croquettes; dip in flour, then egg mixture and breadcrumbs, pressing lightly so breadcrumbs adhere. Makes about 12 croquettes.
In large skillet, heat oil over medium heat 3 minutes or until hot. In batches, add croquettes and cook 6 minutes, turning to brown all sides. Transfer to paper towel-lined cookie sheet to drain. Serve croquettes with dipping sauce.
Approximate nutritional values per serving (1 croquette and about 1½ tablespoons sauce):
378 Calories, 29g Fat (8g Saturated), 91mg Cholesterol, 642mg Sodium, 15g Carbohydrates, 1g Fiber, 13g Protein
Nutritional values are based on data from the USDA National Nutrient Database for Standard Reference. Actual nutritional values may vary due to preparation techniques, variations related to suppliers, regional and seasonal differences, or rounding.