In a bowl, whisk the eggs with the milk, a pinch of salt, and pepper until fully combined.
Heat half the olive oil in a large skillet over medium heat. Add the pulled pork and stir occasionally until warmed through, about 2 minutes. Transfer to a plate and set aside.
Add the remaining olive oil to the same skillet and add the diced onion, cooking for 1 to 2 minutes until it just starts to soften.
Pour in the whisked eggs and let them sit undisturbed for 20 seconds, then push and fold gently with a spatula as they begin to set.
Stir the warmed pulled pork back into the eggs and continue folding until the eggs are mostly set but still slightly glossy.
Add the snap peas and cook for 60 to 90 seconds, folding gently, until they're bright green and still bend rather than snap cleanly in half.
Scatter the cheese over the top and let it melt for about 30 seconds off the heat.
Divide onto plates, top with sliced green onion, and serve immediately while the eggs are still hot.