Mince the garlic, thinly slice the chilies, and wash and thoroughly dry the basil leaves. Have all stir-fry ingredients measured and ready near the stove.
Start cooking the jasmine rice according to package instructions so it’s ready by the time the stir-fry is done.
Heat a large wok or skillet over high heat until very hot. Add a swirl of oil (about 1 tbsp), then immediately toss in the garlic and chilies. Stir-fry for 10–15 seconds until fragrant but not burnt.
Add the ground beef to the wok, breaking it up with a spatula. Cook, stirring frequently, until browned and cooked through, about 3–4 minutes. Drain excess fat if necessary, leaving about 1 tablespoon in the pan.
Pour in the soy sauce, fish sauce, oyster sauce (if using), and sugar. Stir well to combine and let the sauce bubble and reduce slightly, about 1 minute.
Remove the wok from heat and immediately fold in the basil leaves, stirring until they just wilt from the residual heat.
In a separate non-stick pan, heat vegetable oil over medium-high heat. Crack in the eggs and fry until the whites are set and edges are crispy but yolks remain runny (sunny-side up), about 2–3 minutes.
Spoon hot jasmine rice into bowls, top with the basil beef, and place a fried egg on each serving. Garnish with lime wedges and cucumber slices.