Prepare the Prik Nam Pla (dipping sauce) by combining 3 tablespoons of fish sauce, the sliced red chili pepper, and the juice of one lime wedge in a small bowl. Set aside.
Heat a wok or large skillet over high heat. Add the cooking oil and swirl to coat the pan.
Add the minced garlic and stir-fry briefly until fragrant (about 10 seconds), being careful not to burn it.
Push the garlic to the side of the pan and pour in the beaten eggs. Scramble them quickly until they are about 80% cooked.
Add the cold, cooked jasmine rice to the pan. Break up any clumps with your spatula and toss to combine with the eggs and garlic.
Season the rice with 1 tablespoon soy sauce, 1 tablespoon fish sauce, and a pinch of sugar. Stir-fry vigorously for 2-3 minutes to toast the rice.
Gently fold in the lump crab meat and chopped scallions. Toss for another 30-60 seconds just to warm the crab through, being careful not to break the lumps.
Remove from heat immediately.
Serve hot, garnished with cucumber slices, a sprig of cilantro, and a lime wedge. Serve the Prik Nam Pla on the side.