Line a baking sheet with foil, lightly grease and set aside.
Combine 2 tablespoons green onion, hoisin sauce, soy sauce, honey, water, minced garlic, and minced ginger in a small bowl.
Add the pork tenderloin to a large plastic resealable bag. Pour ¼ cup of the hoisin sauce mixture into the bag. Seal and marinate at room temperature for 30 minutes to an hour, turning the bag occasionally. You can also marinate overnight. Reserve the remaining sauce.
Heat a large skillet over medium-high heat, then add 1 tablespoon of vegetable oil. When the oil is hot, carefully remove the pork from the marinade and add it to the pan.
Sear and brown 1 minute on each of the 4 sides, 4 minutes total.
Transfer the seared pork to the sheet tray lined with foil. Bake at 400°F for 20 minutes, or until the internal temperature reaches 140-160°F (depending on the desired degree of doneness).
Begin preparing the carrot puree as the pork is roasting in the oven.
In a medium-sized pot, add carrots, onion, fresh ginger, and garlic.
Cover the ingredients with water, until the water reaches about an inch above. Boil the ingredients until the carrots are tender, about 20 minutes.
Transfer the cooked ingredients and ¾ teaspoon salt to a blender. Blend for 1-2 minutes until smooth.
Add the oil to the puree, and blend for 1 minute. Taste and season with more salt if desired.
Once the pork is removed from the oven, glaze the outside with about a tablespoon of the sauce. Sprinkle with the sesame seeds, so that they adhere to the surface. Allow the pork to rest for 10 minutes. Cut across the grain into thin slices.
Warm the hoisin sauce before serving, either on the stove or in a microwave for about a minute
Add about ¼ cup of warm carrot puree to each serving dish. Place overlapping slices of the meat on top of the puree. Drizzle with warm hoisin sauce. Garnish with freshly sliced green onions. Serve with your favorite vegetable or rice if desired.