Frying eschalot (shallot) and garlic - Slice the garlic and eschalot thinly. Deep fry separately on medium to high heat for one or two minutes or until golden, stirring occasionally. Don't let the garlic burn, otherwise, it'll taste bitter. Remove any excess oil by gently pressing the garlic and eschalot with paper towels. Set aside.
Pour enough water in a saucepan to submerge the eggs by at least one inch. Bring the water to a boil over medium to high heat, then carefully lower the eggs into the water. Room temperature eggs take 5 minutes and refrigerated eggs take 8 minutes to boil for medium cooked eggs. Prepare an ice bath for the eggs by placing water and ice into a bowl. Place the eggs immediately into the ice bath once they're done. Set aside.
Place palm sugar, lemongrass, tamarind, fish sauce and water into a frying pan. Stir to cook over medium to high heat until the sugar dissolves, and the mixture bubbles. Reduce the heat and allow to simmer for 2 to 3 minutes or until the sauce thickens. Remove pan from heat but keep the sauce in the pan to reheat up for later.
Peel the eggs and pat them dry with paper towels. If there is any water left on the eggs, it'll cause the oil to splatter. In a wok or saucepan, pour enough oil to cover eggs, place over medium to high heat. Heat the oil to 170°C (340°F) or test the oil by placing a wooden object into the oil (chopstick, skewer or wooden spoon). The oil is ready for frying if it bubbles around the wooden object. Fry the eggs for 4 minutes or until golden, gently turn the eggs so it cooks evenly. Allow the eggs to rest for a few minutes before slicing them in half. Place the eggs on a serving plate.
Reheat the sauce in the frying pan over medium heat until it is bubbles. If the sauce is too thick, thin it out by adding little splashes of water. It should have the consistency of syrup. Spoon the sauce over eggs and top it with chilli, onion, coriander, fried shallots and garlic. Serve the eggs with rice.