In a small saucepan, bring the water and grated carrots to a light boil over medium heat.
Stir in the rolled oats, minced garlic, and grated ginger, then reduce the heat to medium-low.
Simmer for 5 to 7 minutes, stirring occasionally, until the oats have absorbed most of the liquid and become tender.
Slowly whisk the liquid egg whites into the oatmeal, stirring constantly for 2 minutes to create a creamy, voluminous texture without scrambling the whites.
In a separate small pot of boiling water, cook the two whole eggs for 6.5 minutes for a soft-boiled center, then immediately transfer to an ice bath, peel, and slice in half.
Remove the oatmeal from the heat and stir in the miso paste, nutritional yeast, and tamari until fully incorporated.
Season the oats with sea salt and black pepper to your preference.
Divide the savory oatmeal into bowls, top with the halved soft-boiled eggs, and finish with a drizzle of toasted sesame oil.