Preheat your oven to 425°F (220°C) and line a large sheet pan with parchment paper.
Scrub the Yukon Gold potato and cut it into 1-inch cubes, then trim the ends off the green beans.
Pat the chicken legs dry with a paper towel to ensure the skin gets extra crispy during roasting.
In a large bowl, whisk together the olive oil, minced garlic, chopped rosemary, thyme, sea salt, and black pepper.
Add the chicken legs and potato cubes to the bowl, tossing thoroughly to coat every piece in the herb oil.
Spread the chicken and potatoes onto the prepared sheet pan in a single layer, ensuring they are not crowded.
Squeeze the juice of the half lemon over the chicken and potatoes, then tuck the spent lemon hull onto the tray for extra aroma.
Roast for 20 minutes, then remove the tray briefly to toss the potatoes and add the green beans to the pan.
Return to the oven and roast for another 15-20 minutes until the chicken reaches an internal temperature of 165°F and the potatoes are tender.
Let the chicken rest for 5 minutes before serving to allow the juices to redistribute for a moist and flavorful meal.