Blanch green beans in a large pot of salted water until bright green and crisp tender, about 2 minutes. Shock beans in a large bowl of ice water. Drain and dry well.
In a small bowl, whisk together the shallot, vinegar, and olive oil. Season the vinaigrette with salt and pepper.
Spread baby greens out onto a large platter, top with the cherry tomatoes, green beans, and basil.
Drizzle vinaigrette over the vegetables and sprinkle with pistachios and crumbled feta.