Heat 1 tablespoon butter in a large skillet over high heat for 1 minute, then cook the diced chicken for 4 minutes until golden and cooked to 165°F / 74°C, then transfer to a plate.
Add 1 tablespoon butter to the same skillet and scramble the eggs for 1 minute until just set, then transfer to the plate with chicken.
Add the remaining 1 tablespoon butter and minced garlic to the skillet and cook for 30 seconds until fragrant.
Add the cold rice and frozen vegetables, breaking up any rice clumps, and stir-fry for 3 minutes until the rice is heated through and slightly crispy.
Return the chicken and eggs to the skillet, add soy sauce and sesame oil, and toss for 1 minute until everything is well combined and hot.
Remove from heat, top with sliced green onions, and serve immediately.