Heat oil in a large skillet over medium high heat. Add ginger and cook until fragrant and just starting to brown, 1 to 2 minutes.
Add tomatoes, salt, white pepper, crushed red chili flakes, sesame oil, and oyster sauce. Toss to combine and continue to cook until the tomatoes are jammy, stirring occasionally, 5 to 8 minutes.
In a small bowl, whisk to combine water and cornstarch for the slurry. Pour the slurry into the pan and stir. Allow the tomatoes to continue cooking until broken down and thickened, 2 to 3 minutes. Reduce heat to maintain a simmer.
Drizzle the eggs over the tomatoes and do not stir. Let the eggs gently cook in the tomatoes until just barely set, 2 minutes.
Add the green onions and then gently stir to break up the egg. Don’t stir too much!
Serve the tomato egg with steamed rice and garnish with chopped green onions.
