Heat the cooking oil in a large skillet over medium-high heat. Add the chopped onion and carrot. Sauté for about 5 to 7 minutes until the onions are translucent and the carrots begin to soften.

Add the minced garlic and grated ginger to the skillet. Cook for 1 minute until highly fragrant.

Add the ground beef to the skillet. Cook, breaking up the meat with a wooden spoon or spatula, for 6 to 8 minutes until browned and fully cooked. Drain excess fat if desired.

Sprinkle the Japanese curry powder over the meat mixture. Stir well to coat the beef and vegetables and toast the spices for about 1 minute.

Pour in the beef broth, tomato ketchup, Worcestershire sauce, and soy sauce. Stir thoroughly to combine. Bring the mixture to a gentle boil, then reduce the heat to low. Simmer uncovered for 6 to 8 minutes until most of the liquid has evaporated and the mixture is moist but not runny.

Stir in the frozen peas and cook for 2 more minutes until they are heated through and vibrant green. Taste and adjust seasoning with salt and pepper if needed.

Divide warm cooked rice among plates or bowls, and spoon the beef curry generously over the top. Serve hot.