In a large skillet, melt the butter over medium heat. Add the carrots and sauté, stirring frequently until crisp-tender and beginning to turn golden (8 to 10 minutes).
Add the broccoli and continue cooking for another 4 to 5 minutes. If the skillet begins to dry up, add some of the apple juice while sautéing. When the vegetables are crisp-tender, add the remaining apple juice and sauté, stirring, until it is absorbed. Stir in the lemon juice, chives and pecans. Cook for an additional minute, then transfer to a serving dish and serve immediately.
Notes
If preparing this recipe as GLUTEN-FREE, just be sure to use a brand of apple juice that is known to be GF.