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Place the carrots and 1/4 cup water in a medium saucepan and bring them to a boil over high heat; reduce heat to simmer. Stir, cover, and let carrots simmer another 10-12 minutes or until they are tender.
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Meanwhile, prepare glaze by mixing all glaze ingredients together in a small bowl; set aside. When carrots are done, remove from heat, drain, and set aside.
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Cut tenderloin crosswise into 12 equal slices, and season with salt and pepper. Melt butter in an extra-large nonstick skillet over medium-high heat. Add the pork and cook 2-3 minutes or until nicely browned on the bottom side. Using tongs, flip the pork and cook another 3-4 minutes or until almost cooked through.
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Add carrots to pan with pork. Stir glaze again, and add it to the pan. Bring mixture to a simmer, and cook until pork is done, about 1-2 minutes. Stir to coat pork and carrots with glaze. Divide pork and carrots among 4 plates. Pour any remaining glaze over pork, and garnish with chives, if desired.