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In a small bowl, combine all of the ingredients for the sauce. Set aside.
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For the carrots:
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Put some ice and cold water in a bowl for shocking the carrots after they are blanched.
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Remove the tops from the carrots, slice them in half vertically and blanch them in boiling salted water for 6 minutes.
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Drain the carrots and immediately put them in the bowl of ice water. After 1 minute drain and dry them well.
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Using 1 tablespoon of the olive oil, oil a baking dish large enough to hold all the carrots in one layer (an 8 inch square glass pan or an oval pan will work).
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Spread the yogurt mixture evenly on the bottom of the oiled pan and line up the drained carrots in a single layer. You can trim off the top or bottom of the carrot if it doesn’t fit on top of the yogurt.
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Bake the carrots for 30 minutes. When the carrots are fork tender, remove them from the oven and brush them with the remaining olive oil and sprinkle with the salt and freshly ground pepper. Squeeze the lemon over the top and garnish with the chopped parsley and cilantro.