Heat a large saucepan over medium-high heat. When the pot is hot, swirl in the avocado oil or ghee. Toss in the leeks and shiitake mushrooms.
Cook, stirring for 2 minutes or until the leeks and mushrooms have cooked down, Add the pork and stir-fry until no longer pink.
Stir in the coconut aminos, garlic, and ginger and cook for about 30 seconds or until fragrant. Toss in the bamboo shoots.
Measure out and set aside ½ cup of the broth. Pour the rest of the broth into the saucepan and bring to a boil over high heat. Once the soup is boiling, turn down the heat to medium or lower to maintain a simmer.
Whisk the arrowroot powder into the reserved broth to make a slurry.
In a slow and steady stream, pour the arrowroot slurry into the pot while briskly stirring to thicken the soup. (Note: If arrowroot is overheated, it can break down, so turn off the heat as soon as the soup thickens.)
Remove the pot from the heat. Slowly pour in the beaten eggs while stirring.
Stir in the rice vinegar, sesame oil, and white pepper. Season to taste with salt, and adjust with vinegar or white pepper if desired.
Ladle the soup into serving bowls and garnish with scallions. Serve immediately!