In a small bowl, whisk fish sauce, oyster sauce, regular soy sauce, dark soy sauce, sugar, and water until completely dissolved.
In a mortar and pestle or food processor, pound garlic and chilies into a coarse, fragrant aromatic paste.
Heat 2 tablespoons of oil in a 14-inch wok or very large skillet over high heat until smoking.
Add chili-garlic paste and stir-fry vigorously for 30 seconds until intensely fragrant.⏱ 30 sec
Add minced chicken and spread it across the hot pan, searing for 2 minutes without moving to develop browning.⏱ 2 min
Stir-fry and break up chicken clumps for 3 to 4 minutes until thoroughly cooked through.⏱ 4 min
Pour in prepared sauce and toss continuously for 1 to 2 minutes until glossy and slightly reduced.⏱ 2 min
Turn off heat, add basil leaves, and fold gently for 30 seconds until wilted from residual heat.⏱ 30 sec
In a separate skillet, heat remaining oil over high heat and fry eggs individually until edges are golden and lacy.
Divide warm jasmine rice into four bowls, spoon chicken alongside, and crown each with a crispy fried egg.