Whisk together fish sauce, lime juice, palm sugar, minced chilies, and garlic in a small bowl until the sugar is fully dissolved to create the dressing.
Heat vegetable oil in a wok or small deep skillet over medium-high heat until it begins to smoke slightly.
Crack one egg into a small bowl and carefully slide it into the hot oil; fry until the edges are dark brown, puffy, and crispy (approximately 2 minutes).
Flip the egg gently and cook for an additional 30 seconds ensuring the yolk remains somewhat soft, then drain on paper towels and repeat for the remaining eggs.
Cut the fried eggs into bite-sized wedges, typically 4 to 6 pieces per egg.
In a large mixing bowl, combine the sliced shallots, cherry tomatoes, Chinese celery, and cilantro.
Add the crispy egg pieces to the mixing bowl and pour the dressing over the top.
Toss everything gently but thoroughly and serve immediately while the eggs retain their crisp texture.