Start by peeling the carrots and slicing them into thin rounds. This will help them cook quickly and evenly. Rinse the broccoli florets and set them aside.
In a large skillet, melt the 2 tablespoons of salted butter over medium heat. Allow it to bubble but not brown.
Add the sliced carrots to the skillet. Sauté them for about 5-7 minutes, stirring occasionally, until they begin to soften.
Stir in the 3 cups of broccoli florets. Cook for an additional 3-4 minutes until the broccoli is bright green and tender-crisp.
Pour in 1/2 cup of apple juice and 1 tablespoon of freshly squeezed lemon juice. Stir well to combine and let it simmer for 2-3 minutes, allowing the flavors to meld.
Add the 3 tablespoons of minced chives and 1/2 cup of chopped pecans to the skillet. Season with a dash of salt to taste. Toss everything together and cook for another minute.
Remove from heat and serve warm. This Sauted Broccoli and Carrots with Pecans dish is perfect as a side or light main. Enjoy the crunch and the bursts of flavor!