Melt 1 tablespoon of butter in a large skillet or wok over medium heat. Add chicken and season generously with salt. Cook chicken until browned and no longer pink. Remove from pan and set aside.
Melt ½ tablespoon of butter in same pan and add whisked eggs. Season with salt. Stir frequently until soft scrambled. Remove from pan and set aside.
Melt ½ tablespoon of butter in pan and add sesame oil. Add carrots, peas and the white and light green bottoms of the scallions. Reserve tops of scallions. Season with salt. Cook until carrots begin to soften. Add garlic and cook for about 1 minute more.
Add remaining 1 tablespoon of butter to pan with vegetables and increase heat. Add cold rice and toss in the butter. Stir almost constantly, until rice is heated through, 1-2 minutes. To add extra brown butter flavor, scrape up any browned bits on the bottom of the pan while stirring. If you like crispier rice, let it rest a bit before stirring.
Whisk together soy sauce and oyster sauce and pour over rice in the pan. Stir until sauce is evenly incorporated throughout rice.
Return chicken and scrambled eggs to the pan and stir for a minute until heated through. Stir in the bright green tops of the scallions.
Serve immediately and enjoy!