Set oven rack to lowest position, place sheet pan on rack and preheat oven to 425ºF (218ºC).
In a large bowl, toss 2 pounds roll cut carrots with 1 tablespoon olive oil and 1 teaspoon salt. Carefully remove preheated sheet pan from oven and dump carrots on pan; shake pan to arrange in an even layer then return to oven and roast just until starting to soften, about 20 minutes.
In a small bowl combine 1 tablespoon salt and 2 teaspoons garlic powder. Season 2 tenderloins all over with spice mixture (wait to season the pork until right before you add it to the sheet pan.)
Remove sheet from oven, stir carrots then move carrots around on pan to create two bare strips on sheet pan for tenderloins to fit. Return pan to oven and roast 10 minutes. Remove sheet from oven and sprinkle 8 ounces cubed feta evenly over carrots. Return sheet to oven and continue roasting until tenderloins register 140ºF, 10–15 more minutes.
Meanwhile, mince 1 shallot and add to a medium bowl; fill with cold water and let soak 5–10 minutes. Drain shallots then add back to bowl along with ⅔ cup finely chopped cilantro, 6 tablespoons sesame oil, ¼ cup miso, 3 tablespoons vinegar, 2 tablespoons sesame seeds, 1 teaspoon sugar and ¼ teaspoon salt; whisk to combine.
Transfer pork to a cutting board and let rest 10 minutes. Transfer carrots and feta to a serving platter. Slice pork and arrange over carrots; spoon some sauce over pork, reserving the rest to serve alongside it.
For this recipe, it’s best to use a brewed rice vinegar that is not seasoned (aka no sugar or salt added). If you can’t find that, you can use white wine vinegar or apple cider vinegar instead.
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