Crack the eggs into a medium mixing bowl, add the sesame oil and a small pinch of salt, and beat until slightly frothy. Prepare your tomatoes, garlic, and scallions so everything is ready before you start cooking.

Heat 2 tablespoons of vegetable oil in a wok or large skillet over medium-high heat until shimmering. Pour in the beaten eggs and scramble gently using a spatula until they are just set but still soft and fluffy, about 1 to 2 minutes. Transfer the eggs to a clean plate and set aside.

In the same wok, add the remaining 1 tablespoon of oil. Stir in the minced garlic and the white parts of the scallions, cooking until fragrant for about 30 seconds. Add the tomato wedges and stir-fry until they begin to soften, blister, and release their juices, about 3 to 4 minutes.

Add the soy sauce, sugar, salt, and vegetable broth to the tomatoes, stirring well to combine. Let the mixture simmer for 2 minutes until a rich, natural sauce forms, stirring in the cornstarch slurry during the last minute if you prefer a thicker, glossier gravy.

Return the scrambled eggs to the wok, gently folding them into the tomato sauce so they absorb the savory liquids without breaking apart completely. Garnish with the remaining green parts of the scallions and serve immediately over hot steamed rice.