Put the split peas and 3½ cups (840 ml) of the water in a large pot over high heat. Bring the split peas to a boil, then reduce the heat to medium and simmer, uncovered, for 30 to 40 minutes, until the split peas are tender and most of the water is absorbed. Scoop the cooked split peas from the pot into a small bowl.
In the same large pot over medium heat, combine oil, onions, and additional 1 to 2 tablespoons (15 to 30 ml) water. Cook the onions for 5 minutes, then add the garlic and cook 2 additional minutes, stirring frequently.
Add the split peas, vegetable stock, salt, and pepper and bring the mixture to a boil over high heat. Reduce the heat to medium, add the green tea bags, stir, and simmer, uncovered, for 5 minutes.
Add the green peas and mint, and adjust the temperature as needed to keep the soup at a gentle simmer for 10 to 15 minutes.
Remove the pot from the heat, remove and discard the green tea bags, and let the soup cool for 10 minutes.
Puree the soup using a blender or immersion blender. Season the soup with additional salt, pepper, and/or mint to taste. Add the milk (if using) to make a creamy soup.
Serve the soup garnished with an additional mint leaf.