Preheat the oven to 200 degrees. Peel the parsnip and cut it into even fries. Break off the tough lower ends of the green asparagus.
Distribute the parsnip fries over a baking sheet. Toss them with half a tablespoon of the olive oil. Roast the parsnip in the oven for approximately twenty-five minutes until the fries are cooked through.
Heat the remaining half tablespoon of olive oil in a frying pan when the parsnip is nearly done. Sear the three lamb chops together with the rosemary on high heat until brown on both sides. Add the green asparagus to the pan in the last minute and briefly grill alongside until tender-crisp. Remove the pan from the heat and let the meat rest for a moment.
Remove the roasted parsnip fries from the oven. Distribute the parsnip and grilled green asparagus over a plate. Place the seared lamb chops alongside and serve immediately.