In a medium bowl, combine the turnips, 1 tablespoon of vegetable oil, salt, and pepper.

Heat a large cast-iron pan over medium-high heat.

Coat the hot pan with the remaining 1 teaspoon of vegetable oil.

Add the seasoned turnips to the hot pan.

Reduce the heat to medium.

Toss the turnips frequently to ensure even cooking.

Saute the turnips, shaking the pan, until they start to turn golden brown, particularly on the cut sides and are almost tender, about 8 to 10 minutes.

In a small bowl, whisk together the honey, cayenne, and 1 tablespoon of water.

Pour the honey mixture over the turnips.

Continue to cook, tossing occasionally, until the turnips are tender and glazed, another few minutes.