Combine rice and water (2 1/2 cups for brown rice; 2 cups for white rice) in a medium saucepan with a tight-fitting lid; bring to a boil.
Cover, reduce heat to maintain a gentle simmer and cook until the rice is tender and the water is absorbed (40 to 45 minutes for brown rice; 20 minutes for white).
Remove from heat and let stand, covered, for 10 minutes. Fluff with a fork, spread the rice on a large baking sheet and let cool at least 15 minutes.
This can be done up to 2 days prior.
Thinly slice pork chop crosswise, then cut each slice into long, thin strips about the width of a matchstick. Place a large flat-bottom carbon-steel wok over high heat. Add 2 tablespoons oil and swirl to coat the pan.
Crack one egg into hot wok and cook until soft-cooked. Carefully remove to plate. You can also scramble the egg, if you wish.
Add garlic. Cook, stirring, until just starting to change color, about 20 seconds. Add the pork and cook, stirring, until it is no longer pink, about 2 minutes.
Remove the pork with a slotted spoon to a clean plate. Add the remaining 1 tablespoon oil to the wok. Add mushrooms and cook, stirring, until they soften, 2 to 3 minutes.
Sprinkle in the cooked rice and stir-fry, tossing and then pressing it against the hot wok, then tossing and pressing again, until all the rice has been exposed to the hot wok, about 1 minute.
Add scallions, fish sauce and the cooked pork and cook, stirring, for 30 seconds.
Transfer the fried rice to a platter. Top with soft cooked fried egg. If serving individually, top each serving with one fried egg soft cooked. Garnish with cilantro leaves, lime wedges, thick-cut tomato slices, and cucumber slices.