Place potato in large saucepan and cover with cold water. Bring to a boil. Reduce heat and simmer until potato is fork-tender, about 15 min.
Drain and mash potato. Stir in 3 tbsp (45 mL) of the flour and cream. Stir in cheese, ham and chives, mixing until evenly incorporated. Refrigerate potato mixture until cooled completely, about 30 min
Place remaining 1/4 cup (60 mL) flour, eggs and panko in three separate bowls. Divide potato mixture into bite-size balls. (If the dough is quite sticky, dust hands with flour.) Place each ball in the flour and shake off excess. Then dip each ball into the eggs and roll in panko to coat.
Heat oil in a large saucepan over medium heat until a few breadcrumbs sizzle and bubble immediately when dropped into the oil. Cook the croquettes, turning halfway through, until golden brown, approx. 3 min. Drain on a paper towel-lined plate.