Heat the vegetable oil in a large skillet or pot over medium-high heat.
Add the ground beef and cook, breaking it apart with a spatula, until browned and cooked through, about 5-7 minutes.
Add the diced onion and minced garlic to the pot and cook until the onion is translucent, about 3 minutes.
Stir in the sliced mushrooms and shredded carrots, cooking for another 4 minutes until the vegetables are tender.
Add the frozen peas, soy sauce, brown sugar, rice vinegar, grated ginger, and black pepper to the pot. Stir well to combine all ingredients.
Reduce heat to medium and cook for 3-5 minutes, allowing the sauce to thicken slightly and the flavors to meld.
Remove from heat and serve the beef and vegetable mixture over cooked white rice.
Garnish each serving with sliced green onions.