In a medium-sized stock pot, heat the sesame oil over medium heat. Add the minced garlic and ginger. Sauté until slightly soft and fragrant, about 1-2 minutes.
Add the chicken stock, soy sauce, rice vinegar, green onions, and carrots, and bring to a boil.
Add the frozen dumplings to the pot, bring it back to a boil, reduce the heat to medium-high, and cook for 5-7 minutes or until dumplings are cooked through.
Turn the heat off the pot, add the fresh baby spinach, and stir until the spinach is just wilted but still vibrant green.
Season to taste with sea salt and pepper.
Ladle into serving bowls and garnish with sliced jalapenos, green onions, and a wedge of lime.