Prepare the Prik Nam Pla (dipping sauce) by combining the chopped red chili pepper, 3 tablespoons fish sauce, and juice from 1 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.
Add the minced garlic and sauté briefly until fragrant (about 10 seconds), being careful not to burn it.
Push the garlic to one side and pour the beaten eggs into the empty space. Scramble them quickly until mostly set, then mix with the garlic.
Add the cold, day-old jasmine rice to the wok. Break up any clumps with a spatula and toss to combine with the egg and garlic.
Pour in the soy sauce, 1 tablespoon fish sauce, and sugar. Stir-fry constantly for 2-3 minutes until the rice is hot and evenly coated.
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, cilantro, and a lime wedge. Offer the Prik Nam Pla on the side for spooning over the rice.