Begin by heating a large stock pot over medium-high heat. Add sesame oil and let it shimmer, then toss in chopped sweet onion, minced garlic, sliced carrots, and grated fresh ginger. Sauté for about 5-7 minutes until the vegetables are tender and slightly caramelized.

Pour in equal parts chicken and beef broths along with some water, stirring to combine. Increase the heat to bring the mixture to a rolling boil, then reduce to maintain a low boil. Cover and let simmer gently for at least 1 hour.

After an hour of simmering, carefully remove the solid vegetables from the broth using a skimmer or fine-mesh strainer. Taste the broth, adjusting the salt as needed.

Ladle the warm broth into bowls, garnishing with finely chopped scallions and thinly sliced button mushrooms. Enjoy warm!