In 12-inch skillet, melt margarine or butter on medium-high.
Add shallot and cook 2 minutes or until golden and tender, stirring occasionally.
Add radishes and turnips; stir until well coated.
Stir in water, broth, honey, 1/4 teaspoon salt, and 1/4 teaspoon freshly ground black 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. Transfer to serving platter and garnish with mint leaves.