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Preheat the oven to 375 degrees F.
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Combine the quinoa, thyme, and vegetable stock in a small saucepan and bring to a simmer. Simmer quinoa for 12-15 minutes until all liquid is absorbed and quinoa is tender. When cooked, remove from the heat, remove the thyme stems, and set off to the side to slightly cool.
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Coat sliced carrots in olive oil and lay cut side down on a baking sheet. Roast in the oven for 30 minutes.
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In a small mixing bowl, whisk together the honey vinegar, garlic, salt, pepper, olive oil, mustard, lemon zest, and lemon juice. Set off to the side.
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When carrots are done roasting, remove from the oven, and place off to the side to slightly cool.
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In a large bowl or on a large serving platter, toss together the chives, red onion, arugula, parsley, and quinoa. Top the salad with the roasted carrots and the dressing and then serve.