In a large stainless steel skillet over high heat, heat 1 tablespoon oil and swirl to coat skillet. Add beef and break into small pieces with wooden spoon to create a single layer; season with salt. Cook, stirring occasionally, until beef is cooked through and starting to get a brown crust, 5 to 6 minutes. Using a slotted spoon, transfer beef to a plate.

Meanwhile, in a small bowl, whisk oyster sauce, soy sauce, molasses, fish sauce, sugar, and ¼ cup water until sugar is dissolved.

Reduce heat to medium-high. In same skillet, cook bell pepper, carrots, a pinch of salt, and 1 tablespoon oil, stirring occasionally, until peppers begin to soften, about 5 minutes. Add chiles and cook, stirring, until starting to soften, about 2 minutes. Add white scallion parts, garlic, and ginger and cook, stirring occasionally, until fragrant, 1 to 2 minutes more.

Pour sauce into skillet and bring to a simmer. Cook, stirring occasionally, until sauce is thickened and glossy, 3 to 4 minutes. Reduce heat to low and add basil. Cook, stirring, until basil is wilted, about 2 minutes. Return beef to pan. Toss until beef is coated with sauce. Top with green scallion parts.

In a small nonstick skillet over medium heat, heat remaining 2 tablespoons oil. Crack eggs into pan and cook until whites are set, 3 to 4 minutes; season with salt.

Divide rice among bowls. Top with beef, sauce, and an egg.