In the meantime, make the dressing by whisking together the mustard, vinegar, 1 tablespoon olive oil, the sugar, and 1/4 teaspoon salt in a bowl. Alternatively, combine the ingredients in a mason jar and shake until blended. Taste and adjust if needed.
In a large skillet, saute the dill in a splash of olive oil over medium-high heat. Add a couple pinches of salt, stir in the leek, and saute until golden and slightly crispy, 4 to 5 minutes.
In a large bowl, gently toss the potatoes and green beans, celery, cucumber, tofu, chives, and half of the leek with most of the dressing. Taste, and add a sprinkling of salt, if needed. Turn out onto a platter and finish with a final drizzle of dressing and the remaining leek. Serve chilled or at room temperature.