Spread chilled cooked rice on a sheet pan and break up any clumps with your hands.
Heat 1 tablespoon butter in a wok or large skillet over high heat until foaming.
Add diced carrots and chopped onion; stir-fry about 3 minutes until beginning to soften and lightly color.
Push vegetables to one side; add another tablespoon butter to the empty side. Pour in beaten eggs, let sit 30 seconds, then scramble and mix with vegetables.
Add the cold rice, breaking up any remaining clumps as you stir everything together.
Stir in frozen peas, minced garlic, salt, and black pepper; cook about 2 minutes, stirring constantly.
Pour soy sauce and oyster sauce around the edges of the pan (not directly on the rice) and stir vigorously for 1 minute until absorbed and evenly colored.
Remove from heat; add the remaining 1 tablespoon butter and drizzle in toasted sesame oil. Toss to coat, then fold in sliced green onions.
Portion immediately into 5 meal prep containers while still warm, leaving lids slightly ajar to vent until cooled to room temperature.
Once completely cool (about 30 minutes), seal containers and label with the date. Refrigerate promptly.