In a sauce pot add the stock, water, lemongrass, garlic, chili paste, and a couple inches of thick-sliced ginger. Bring to a boil; reduce heat to simmer and cover, steeping the flavor into the broth for 5 to 6 minutes.
Strain the broth or skim out the flavorings with a slotted spoon. Reduce the heat to low and slice 1-inch peeled ginger into thin matchsticks and stir into the clear broth with the mushrooms.
Beat the eggs and then swirl slowly into the broth to create egg ribbons. Wilt in the chard. Remove from heat and serve in bowls immediately.