Preheat the oven to 375 degrees F. Spread the hazelnuts on a baking sheet and bake until toasted, about 7 minutes. Let cool slightly, then rub with a kitchen towel to remove the skins; roughly chop and set aside.
Fill a large bowl with ice water and set aside. Bring a large pot of salted water to a boil. Add the haricots verts and cook until crisp-tender, 5 to 7 minutes. Drain and immediately transfer to the ice bath; let sit until cool, about 2 minutes. Drain and pat dry.
Melt the butter in a large skillet over medium heat and cook, stirring occasionally with a rubber spatula, until golden brown flecks appear and the butter smells nutty, about 4 minutes. Add the hazelnuts and cook 30 seconds. Remove the hazelnuts and all but 2 tablespoons of the browned butter to a small bowl; cover to keep warm.
Add the broth to the skillet and season with 1 teaspoon salt. Bring to a boil over high heat, then add half of the haricots verts and cook until warmed through, about 2 minutes. Transfer to a platter using tongs. Repeat with the remaining haricots verts. Top with the hazelnuts. Season with salt and sprinkle with the lemon zest.