Have every ingredient measured and within reach. Break the cold rice into individual grains with your fingers. Pat the shrimp dry.
Heat a wok over high heat until smoking. Add 1 tablespoon oil, swirl, and sear the shrimp in a single layer 1 minute per side until pink and curled. Transfer to a plate.
Reduce heat to medium. Add the remaining 1 tablespoon oil, then the tom yum paste, chili jam, lemongrass, galangal, lime leaves, and bird's eye chilies. Stir-fry 1 to 2 minutes until fragrant and the oil turns deep red-orange.
Add the mushrooms and stir-fry 2 minutes until softened and colored by the paste.
Push everything to the sides. Pour in the beaten eggs, let set 15 to 20 seconds, then scramble into soft curds and fold together.
Add the day-old rice. Toss and press against the hot wok, resting 30 seconds between tosses, 4 to 5 minutes, until every grain is coated and heated through.
Drizzle in the fish sauce, lime juice, and sugar. Return the shrimp and scallion whites; toss 1 minute more. Taste and adjust lime and fish sauce.
Divide among four bowls. Top with scallion greens, cilantro, and lime wedges. Serve with extra fish sauce and sliced chilies.