Steam the potatoes and carrots until almost tender (steamer rack set over simmering water), about 9 minutes. Add the broccoli florets to the steamer rack; cover and steam until all vegetables are just tender, about 3 minutes. Transfer the vegetables to a large bowl and cool to room temperature.
Mix the hoisin and honey in a small bowl. Brush the roasted chicken with the honey-hoisin mixture. Add the chicken and red onion to the bowl of vegetables.
PREPARE THE DRESSING:
Combine the oil and garlic in a small saucepan. Cook over low heat just until garlic begins to sizzle, about 1 minute. Remove from heat and cool slightly. Whisk in the lemon juice and thyme. Pour the warm dressing over the salad and toss to coat. Season salad to taste with salt and pepper.