Stir the oyster sauce, soy sauce, dark soy, fish sauce, sugar, and water together in a small bowl. Set it by the stove so you are not measuring mid-stir-fry.
If you want fried eggs, heat 1 tablespoon oil in a nonstick pan over medium-high and fry the eggs until the edges are crisp and lacy but the yolk is still runny. Slide onto a plate and set aside.
Heat the remaining 1 tablespoon oil in a wide skillet or wok over high heat until it shimmers. Add the garlic, bird's eye chilies, sliced red chili, and shallot. Stir for about 30 seconds, just until fragrant, do not let the garlic brown.
Add the ground beef. Spread it flat and let it sit for a minute to sear before you break it up. Keep the heat high and cook 6 to 8 minutes, breaking the meat into small pieces, until any liquid has cooked off and the beef starts to crisp at the edges.
Pour in the sauce and toss for about 1 minute until it coats the beef and mostly evaporates.
Turn off the heat. Add the basil and fold it through just until wilted, 15 to 20 seconds. Taste and adjust with a little more fish sauce or sugar. Serve over jasmine rice with a fried egg on top.