Blanch the shrimp by bringing a pot of water to boil, then add the shrimp. As soon as the shrimp turn pink and start curling, scoop them out and drain. Set aside.
Place the eggs, 1/2 teaspoon of salt, the white pepper, and 1 tablespoons of chopped scallions in a medium bowl. In a separate bowl, whisk the arrowroot starch with a little less than 1 tablespoon of water and add the egg mixture and gently whisk. Add the shrimp to the egg mixture.
Heat a large skillet over medium-high heat, add 1 tablespoon of ghee, and lower the heat to medium. Add the shrimp and egg mixture. Gently stir-fry until the eggs are about 70 percent cooked, similar to soft, runny scrambled eggs. Scoop the mixture out of the pan and set aside.
Add the remaining 1/2 tablespoon of ghee to the skillet, then add the remaining 3 tablespoon of scallions, the chopped tomato, and the tomato paste. Season with a small pinch of salt. Sauté for about 10 seconds. Add the shrimp and egg back to the pan and give a quick toss, about 5 seconds.
Serve hot with cauliflower rice. Drizzle with sesame oil and top with more scallions, if desired.