Preheat the oven to 400°F.
Place the potatoes on a baking sheet. Drizzle with 2 tablespoons of EVOO and season with salt and freshly ground black pepper. Roast in the oven for 20-25 minutes. In the last 15 minutes of cooking time, add the green beans to the baking sheet with the potatoes.
While the potatoes are roasting, combine the apples, brown sugar and apple juice in a medium-size pot over medium-high heat and cook, stirring occasionally, until a chunky sauce forms, about 10-12 minutes. If the sauce begins to spatter as it bubbles, reduce the heat. Once a sauce forms, remove the pot from the heat.
Preheat a large skillet over medium-high heat with 2 turns of the pan of EVOO.