Rinse the jasmine rice in a fine-mesh strainer under cold running water for about one minute, until the water runs mostly clear.
In a large pot, bring 5 cups of water to a boil. Then, add the jasmine rice and simmer over medium-low heat with the lid partially open, stirring occasionally to prevent sticking. Cook for 25 minutes until the rice starts to break up. Use a whisk and break up the rice. Continue simmering for an additional 10 to 15 minutes, or until it reaches your desired consistency. If the congee gets too thick, add some hot water to thin it out.
While the congee is simmering away, combine the ground pork, soy sauce, white pepper, brown sugar, and toasted sesame oil in a bowl. Marinate until you are ready to add the pork meatballs to the congee.
To make the meatballs, take about a tablespoon of the mixture, cup it in your palm, and roll it between your hands until you form a ball.
Add the ginger slices and the pork meatballs to the bubbling congee. Cook until the meatballs are done, about 8 to 10 minutes.
Taste and season with sea salt to taste. Stir in the sliced green onions and serve.