How to Make It
Whisk together olive oil, vinegar, sugar, salt, and pepper in a medium bowl. Set aside.
Bring 8 cups water to a boil in a large saucepan over high. Add haricots verts and wax beans; cook until crisp-tender, about 5 minutes. Drain and transfer beans to a bowl of ice water. Let stand until chilled, about 10 minutes. Drain and set aside.
Heat canola oil in a large skillet over medium-high. Add edamame and sugar snap peas; cook, stirring occasionally, until lightly charred, about 3 minutes. Cover and cook until peas are tender, about 1 minute.
Add edamame mixture, cannellini beans, celery, onion, and parsley to olive oil mixture; toss to coat. Add chilled green beans and wax beans; toss to coat before serving.