Preheat oven to 400 degrees and prepare a baking sheet with foil. In a mixing bowl, combine hoisin, brown sugar, half of soy sauce, and half of ginger. Rinse pork tenderloin, pat dry, and combine and brush with marinade. Set aside while you prepare remaining ingredients.

Thoroughly rinse produce and pat dry. Trim and thinly slice green onions at an angle (bias), keeping white and green portions separate. Stem shiitake mushrooms and slice caps into thin strips.

Heat 1 tsp. olive oil in a medium pan over medium-high heat. Remove pork from marinade and blot off excess marinade. (Reserve marinade to use as sauce in Step 5.) Add tenderloin to pan and sear until caramelized on all sides, about 6-8 minutes total. Place tenderloin on prepared baking sheet and cook 15 minutes or until a minimum internal temperature of 145 degrees is reached. Let rest before slicing. Resting cooked meats allows the juices to redistribute, which means a juicier, more flavorful final product. Wipe pan clean for broccoli step.

In a medium pot, add 2 1/2 cups water, sliced shiitake mushrooms, remaining soy sauce, remaining ginger, chicken base, and whites of green onion. Bring to a simmer and cook 15 minutes. Mix half of cornstarch with 1 Tbsp. cold water and combine remaining cornstarch with liquid eggs. Add water-cornstarch mixture to pot and stir. Reduce heat to barely a simmer. Hold a fork over pot and slowly pour liquid eggs in a stream through the tines. This technique helps achieve the egg "ribbons" that are traditional for this soup. Allow to simmer 1 more minute to set eggs, then remove from heat. Soup should be glossy and rich.

Bring pan from previous step with 3 Tbsp. water and a pinch of salt to a boil over high heat. Add broccoli florets and cover. Let broccoli steam for 2 minutes until bright green and fork-tender. Drain any excess liquid and move broccoli to a plate. In same pan, add reserved marinade and bring to a boil over medium-high heat. Cook for two minutes and prepare to serve.

Slice tenderloin into 1/2" pieces and serve on a plate next to broccoli florets. Serve egg drop soup in a small bowl on side and garnish with remaining green onion. Add sauce in front of pork and serve.