Heat a 14-inch flat-bottomed wok over high heat until a bead of water vaporizes within 1 to 2 seconds of contact. Swirl in 2 teaspoons oil, coating the bottom completely. Add beaten eggs and cook, tilting to cover the surface as thinly as possible to make an egg pancake. When the pancake is just set, 30 seconds to 1 minute, flip using a metal spatula and allow it to set for about 5 seconds. Transfer to a cutting board. Cut into bite-size pieces.
Swirl 1 tablespoon oil into the wok, add garlic and shallots and stir-fry, using a metal spatula, until fragrant, 10 seconds. Add parsnips and Brussels sprouts, reduce the heat to medium-high and stir-fry until the vegetables are nearly cooked through, about 2 minutes. Swirl in the remaining 1 tablespoon oil, add rice, tomatoes and soy sauce and stir-fry, breaking up the rice, until heated through, 2 minutes. Sprinkle with cilantro, salt and pepper; add the egg pieces and toss to combine.