In a large bowl, whisk together the olive oil, vinegar, mustard, orange juice, maple syrup and garlic. Take out 2 tablespoons of the vinaigrette and reserve in a separate small bowl for marinating the carrots.
Add the parsley, oregano, red pepper flakes and salt to the large bowl of vinaigrette and whisk until well combined. Fold in the yogurt and set aside.
In a large cast iron or grill pan over medium-high heat, sauté the chorizo until browned and just starting to become crispy. Reserve on a plate.
Trim the greens from the carrots, leaving about an inch of green on top of each carrot. Reserve the greens for garnishing. Trim any excess from the root end of the carrots. Slice the carrots in half lengthwise. Toss the carrots with the reserved vinaigrette.
When all the carrots are cooked, arrange on a platter and drizzle with chimichurri yogurt sauce.
Chop the reserved carrot greens and sprinkle on top.