In a small mixing bowl, whisk together oyster sauce, soy sauce, fish sauce, brown sugar, and water. Set aside.

Heat 1 tablespoon oil in grill or cast iron skillet over high heat. Add ground chicken and cook for 4-5 minutes on cutting board, breaking it up with a wooden spoon, until browned and cooked through. Transfer to a plate.

In the same skillet, add remaining tablespoon of oil. Add minced garlic, sliced chilies, and shallot. Stir-fry for 1 minute using tongs until fragrant and garlic is golden.

Add diced red bell pepper and stir-fry for 1 minute until slightly softened.

Return cooked chicken to the skillet. Pour sauce over everything and toss for 1-2 minutes until well combined and chicken is coated.

Remove from heat and stir in Thai basil leaves. The heat from the pan will wilt them perfectly. Set aside and keep warm.

In a separate small skillet, heat 2 tablespoons oil over medium-high heat. Crack eggs one at a time and fry for 2-3 minutes until edges are crispy and lacy but yolk is still runny. Use tongs carefully to transfer.

To serve: Divide hot jasmine rice among 4 bowls. Top each with Thai basil chicken and a crispy fried egg. Serve with lime wedges and cucumber slices on the side.