In a medium bowl combine cheese and flour; set aside.
In a Dutch oven combine the carrot, curry powder, and paprika. Cook and stir over medium heat for 2 minutes. Stir in milk. Cook, uncovered, for 4 to 5 minutes or just until milk is hot but not boiling, stirring occasionally. Gradually whisk in mashed potatoes. Cook and stir until hot and bubbly. Stir in the cheese and flour. Cook and stir about 2 minutes or just until cheese melts.
Using shamrock cookie cutters, cut shamrocks out of slices of bread. Toast the shamrocks and top with prepared pesto.
Ladle soup into bowls. Top with one pesto-topped toast shamrock per bowl.