Heat 3 tablespoons vegetable oil on a griddle. Pan fry cubed radish cake until lightly brown in color, about 8 to 10 minutes. Push browned radish cake to one side of griddle.
Add 1 tablespoon vegetable oil on the cleared side of griddle. Sauté ¼ of the chai poh (pickled radish), ¼ of the garlic, and 1 teaspoon of chili paste for 30 seconds.
Push ¼ of the fried radish cake towards the sauteed chai poh, garlic, and chili paste. Mix well with a spatula.
Create a well in the center of the fried radish cake. Add shrimp in the well and let it cook until shrimp turn pink or curl, about 1 to 2 minutes. Push shrimp away from the well.
Crack an egg into the well. Add ¼ of the chives, 1 teaspoon soy sauce, salt and ground pepper to taste. Stir and toss fried radish cake over the egg and stir fry to combine, about 2 minutes.
Remove and serve immediately. Repeat with the remaining 3 portions of fried radish cake.