How to Make It
In a blender, combine the egg with the lemon zest and juice, Dijon mustard, garlic and water and puree until smooth. With the machine on, drizzle in the vegetable oil and 3/4 cup of the olive oil until emulsified. Scrape the aioli into a bowl and stir in the minced chives and dill. Season the aioli with salt and pepper. Refrigerate until chilled, about 30 minutes.
Meanwhile, in a large saucepan of salted boiling water, blanch the green and yellow beans until they are just crisp-tender, about 2 minutes. Drain and cool under running water; pat thoroughly dry.
Light a grill and put a perforated grill pan on it to heat. In a large bowl, toss the beans with the shallots and the remaining 1 tablespoon of olive oil; season with salt and pepper. Spread the beans on the grill pan and grill over high heat until lightly charred on the bottom, about 3 minutes. Toss and grill for 30 seconds longer. Transfer the beans to a bowl and garnish with dill and parsley sprigs. Serve with the aioli.