In a large bowl, mix the meatball ingredients by hand. Roll mixture into 25-30 1" meatballs.
Heat a dutch oven over medium heat and drizzle about 1 Tbsp of olive oil.
Brown half the meatballs and transfer to a plate. Repeat with the remaining meatballs.
Pour broth into the dutch oven and stir to deglaze the bottom of the pot.
Add the carrots and meatballs to the broth. Bring to a boil, then reduce to a simmer. Simmer for 30 minutes, or until the meatballs are cooked through.
Add in the chopped spinach and simmer for an additional 15 minutes.
Stir the soup rapidly while slowly pouring in the whisked egg. Be sure to keep stirring the soup to prevent the egg from clumping in the soup. The egg should look like long strings in the soup.