In a small bowl, whisk together the fish sauce, light soy sauce, oyster sauce, dark soy sauce, palm sugar, and water until the sugar dissolves; set aside.
Stem the Thai chiles and peel the garlic. Pound them together in a mortar and pestle to a coarse paste (or finely chop). Pick the holy basil leaves and set aside.
Heat a wok or large skillet over high heat until very hot, 2–3 minutes. Add the vegetable oil and swirl to coat.
Add the garlic–chile paste and stir-fry until fragrant but not browned, 15–30 seconds.
Add the ground beef, spreading it out in the pan. Let it sear undisturbed for 30 seconds, then stir-fry until just cooked through with browned edges, 2–3 minutes.
Pour in the sauce mixture around the sides of the wok. Toss and stir-fry until the liquid reduces, turns glossy, and coats the beef, 1–2 minutes.
Turn off the heat and add the holy basil leaves. Toss until just wilted, 10–20 seconds.
Serve the beef kaprow over hot steamed jasmine rice and top each portion with a fried egg if using. Serve immediately.