Heat a large cast iron pan over medium-low heat. Add pine nuts and cook, shaking the pan, until toasty and lightly golden, 3-5 minutes. Transfer to a bowl.
In the same pan, heat olive oil and butter over medium-high heat until melted. Add green beans, season with salt and pepper and toss to coat. Cook undisturbed until browned in spots, 3-5 minutes. Use tongs to flip beans and continue to cook, tossing once or twice, until beans are charred and tender, about 5 minutes. Season with more salt and pepper if needed.
Remove from heat and stir in lemon zest, parmesan and toasted pine nuts. Serve warm.