Toss turnips with 1 tsp. oil, salt and pepper in a medium bowl.
Combine honey, cayenne and water in a small bowl.
Heat a small skillet over medium-high heat. Add remaining tsp. oil. Add turnips. Sauté for about 10 minutes, turning turnips frequently, until they are golden brown.
Add honey mixture to turnips and toss them for a few minutes until glazed and tender. Add additional salt and pepper to taste.