Make the honey-hoisin sauce: In a small bowl, whisk together the hoisin sauce, soy sauce, honey, garlic, ground ginger and 2/3 of the chopped green onions.
Reserve and refrigerate 1/4 cup of the honey-hoisin sauce. Place the rest of the sauce in a large zip-top bag and add the pork tenderloin. Seal the bag and place in the refrigerator to marinate the pork for 30 minutes or overnight.
Preheat oven to 400 degrees F.
Heat 1 tablespoon of the olive oil in an oven safe skillet over medium-high heat. I use my cast iron skillet. (If you do not have an oven safe skillet, you can transfer the pork to a baking dish after browning it on the stove.) When the pan is hot, add the pork tenderloin and brown on all four sides, 1-2 minutes per side. (Discard any marinade left in the zip-top bag, since it touched the raw pork.) Remove pan from the heat.
With the pork tenderloin along the center of the pan, add the carrots on either side of the pork. Drizzle carrots with the remaining 1/2 tablespoon olive oil and toss to coat. Sprinkle with salt and pepper.
Transfer the skillet to the oven and roast for 12 minutes. Stir the carrots and drizzle half of the remaining honey-hoisin sauce over the pork.
Continue to roast the pork and carrots in the oven for 8-13 more minutes, until an instant-read thermometer inserted into the thickest part of the pork registers 145 degrees F.
Remove from the oven and let pork rest for 5-10 minutes before slicing and serving. Serve pork with the remaining honey-hoisin sauce and chopped green onions, with the carrots on the side.