In 12-inch skillet, melt butter on medium-high. Add onion and cook 2 minutes or until golden and tender, stirring occasionally. Add radishes and turnips; stir until well coated. Stir in broth, honey, salt and pepper. Heat to boiling. Reduce heat to medium-low; cover and cook 15 minutes.
Uncover and cook 7 to 10 minutes longer or until vegetables are glazed and most of liquid has evaporated, stirring occasionally. Remove from heat and stir in mint and chives.