Step 1
Place a rack in middle of oven; preheat to 400°. Arrange 6–8 thin slices prosciutto on a parchment-lined baking sheet, overlapping by no more than ½” if needed, and bake until crisp, 7–9 minutes. Let cool.
Step 2
Meanwhile, cook 2 lb. green beans, trimmed, in a medium pot of boiling generously salted water until bright green and crisp-tender, about 4 minutes. Drain beans; transfer to a large bowl of ice water and let cool. Drain green beans and thoroughly pat dry with a kitchen towel or paper towels. Set aside.
Step 3
Cook ⅔ cup extra-virgin olive oil and ½ cup coarsely chopped blanched hazelnuts in a medium skillet over medium heat, stirring often, until hazelnuts are golden brown, 5–7 minutes. Immediately transfer nuts and oil to a large bowl; reserve skillet. Let cool until just barely warm, about 10 minutes.
Step 4
While nuts and oil are cooling, cook 12 Medjool dates, pitted, quartered lengthwise, in reserved skillet over medium-high heat, tossing occasionally and adding up to 2 tsp. more extra-virgin olive oil if pan is dry, until lightly charred in spots, about 2 minutes. Transfer dates to a plate.
Step 5
Add 1 large shallot, finely chopped, 3 garlic cloves, finely chopped, zest of 1 medium lemon, ¼ cup fresh lemon juice, ¼ cup red wine vinegar, 2 Tbsp. honey, 2 tsp. Dijon mustard, and 1 tsp. Diamond Crystal or ½ tsp. Morton kosher salt to bowl with nuts and oil and whisk to combine; generously season vinaigrette with freshly ground pepper.
Step 6
Add dates and reserved green beans to vinaigrette and toss to coat. Taste and season with more salt and pepper if needed. Transfer green bean mixture to a platter or large shallow bowl. Crumble prosciutto into small shards and scatter over green bean mixture.
Do Ahead: Prosciutto can be baked 4 hours ahead; store, loosely covered, at room temperature. Green beans can be blanched 1 day ahead; pat dry, transfer to an airtight container and chill. Nuts can be cooked 1 day ahead; transfer to an airtight container along with oil and store at room temperature.