Position oven racks in the top and bottom thirds of the oven. Heat the oven to 450°F.

Put the beans in a large bowl. Peel the garlic, quarter each clove lengthwise (if the cloves are small, halve them), and add them to the green beans. Toss the beans and garlic with 1/4 cup of the olive oil, 1 Tbs. of the lemon zest, 1 tsp. salt, and 1/2 tsp. pepper.

Spread the beans on a rimmed baking sheet and roast in the top third of the oven for 10 minutes. Stir the beans and garlic with a spatula for more even cooking and coloring. Continue roasting until the beans and garlic pieces are lightly browned and tender throughout, another 10 to 15 minutes.

Meanwhile, spread the pine nuts out on a rimmed baking sheet and toast in the bottom third of the oven until just golden, about 5 minutes

Transfer the beans to a small serving platter or shallow bowl and dress with the lemon juice and the remaining 2 Tbs. olive oil. Toss gently to coat and season to taste with salt and pepper. Sprinkle on the toasted pine nuts, the remaining 1/2 Tbs. lemon zest, the Parmigiano, and the parsley. Serve hot or at room temperature.