Step 1Whisk together the vinegar, mustard and sugar in a small bowl. Slowly whisk in the oil until emulsified. Stir in the shallot and salt and pepper to taste. Set aside.
Step 1Steam the artichokes over simmering water until tender but still firm, 10 to 15 minutes. Drain and toss with the oil and salt and pepper to taste. Set aside.
Step 2Heat a grill or stove-top grill pan over high heat. Grill the artichokes, turning once or twice, until they are lightly charred, about 5 minutes.
Step 3Steam the green beans over simmering water just until bright green and crunchy, 3 minutes. Drain, refresh in ice water, then drain again and set aside.
Step 4Toast the almonds in a small skillet over medium heat, stirring frequently, until golden, about 5 minutes.
Step 5Toss the artichokes, green beans, almonds, chicken and mixed greens together in a large bowl with the dressing.