Heat the olive oil in a large skillet over medium-high heat. Add the mustard seeds and let cook 2 minutes. Add the cumin seeds and curry leaves, if using, and sauté 1 minute. Add the onion and sauté while stirring for a minute. Add the turmeric, sauté, stirring frequently, about 3 minutes, until the onion is translucent. Cover and cook, stirring regularly, until the onion is golden and caramelized, 7-8 minutes.
Add the mung beans to the skillet. Mix thoroughly until they are coated with the spice and onion mixture. Add the tomatoes and the sea salt, stir well, and continue cooking, covered, for an additional 4-5 minutes. Add the chili pepper and the garlic-ginger paste, if using, and stir well. Add the garam masala and continue cooking for one minute. Add the vegetable broth and bring to a boil. Reduce the heat to medium-low, cover and cook until the beans are tender, about 35-40 minutes. Add the coconut milk and adjust spices and salt. Let reduce until the desired consistency, over a medium flame. Remove to a serving bowl. Garnish with fresh cilantro and lemon or lime juice. Bon appétit!