Heat 1 tablespoon sesame oil in a large nonstick skillet over medium heat. Add the carrots and cook, stirring occasionally, until just tender, about 3-4 minutes. Season with salt and pepper. Transfer to a bowl. Do Ahead: The carrots can be made up to 1 hour in advance. Serve warm or at room temperature.

In the same skillet, heat the remaining tablespoon of sesame oil over medium-low heat. Add the garlic. Cook, stirring, until just fragrant, about 1 minute. Pile in the bok choy and season with salt, pepper and a pinch of gochugaru or red pepper flakes. Increase the heat to medium. Cook, stirring occasionally, until the bok choy is crisp tender, about 3 minutes. Remove the pan from the heat and add the lime juice. Season with salt and pepper to taste. Do Ahead: The bok choy can be made up to 1 hour in advance. Serve warm or at room temperature.