The most-cooked dish in China, with shrimp folded in. Everything hinges on three small decisions: sugar to tame the tomato's acid, eggs pulled while still wet, and shrimp that leave the wok before they're done.
Sugar isn't a sweetener here, it's a corrector. Supermarket tomatoes are acidic and underripe, and without a teaspoon or two the dish tastes thin and sour no matter how good your eggs are. Add it early, with the tomato jelly, so it has time to cook in.
Cook everything separately, then reunite it. Shrimp, eggs, and tomatoes all want different heat and different timing — crowding them into one pan means watery eggs and grey shrimp. Three quick passes in the same wok take ten minutes total.
Splitting the tomato into jelly and flesh is the trick that separates a good version from a soupy one. The seedy interior carries almost all the water and glutamate — cook it down hard into a sauce, and the wedges stay intact instead of collapsing.
Frozen shrimp are fine, and often better than the "fresh" ones at the counter, which were usually frozen anyway. Thaw them in cold salted water, then dry them well — wet shrimp steam instead of searing.
Variation — with yu choy, no egg (番茄蝦仁油菜). Blanch 8 oz of yu choy cut into 2-inch lengths: stems into salted boiling water for 45 seconds, leaves for the last 15, then shock in ice water and squeeze dry. Going in raw, they release enough water to undo the sauce you just reduced. Fold them in for the final 15 seconds so they stay green.
Dropping the eggs leaves nothing to absorb the sauce, so rebalance: raise the shrimp to 12 oz, add 3 tbsp chicken stock along with the tomato jelly, and finish with 1 tsp cornstarch slaked in 1 tbsp water so the sauce clings rather than pools. Keep the sugar — without the eggs to soften it, the tomato's acid comes through sharper, not less.