Green beans: Bring a large saucepan of heavily salted water (as "salty as seawater") to a boil over high heat. Meanwhile, prepare an ice bath in a large bowl. When the water is boiling, add the green beans and cook until just crisp-tender and bright green, 3–4 minutes. Use the strainer to immediately transfer them to the ice bath to stop the cooking. Set aside while you make the vinaigrette. (Note: Green beans can be blanched 1 day ahead. After cooling, drain, wrap in a clean dish towel, and store in the refrigerator.)
Vinaigrette: In a small bowl, stir the honey and vinegar together with a small rubber spatula. Add the hazelnut oil in a slow stream, whisking constantly, until all the ingredients are combined. Season with salt and pepper, whisking as you go and tasting between additions.
Assemble: Line a bowl with paper towels. Transfer the cooled green beans from the ice bath into the bowl; pat them dry and remove paper towels. Spoon half of the vinaigrette over the green beans and use your hands to mix well; taste, then add more vinaigrette as needed. Season with salt and pepper, then transfer to a serving plate.
Garnish: Stack the basil leaves, then roll the stack like a cigar. Finely slice crosswise to create thin ribbons of basil. (This is called a "chiffonade.") Top the green beans with the basil, followed by the hazelnuts; finish by zesting the lemon directly over the green beans. Serve immediately.