Step 1
Stir 3 Tbsp. Japanese curry powder, 3 Tbsp. ketchup, 2 Tbsp. pure maple syrup, 2 Tbsp. white miso, and 1 Tbsp. soy sauce in a small bowl to combine; set sauce aside.
Step 2
Heat 3 Tbsp. vegetable oil in a large skillet, preferably cast-iron, over medium-high. Add 1 large white onion, finely chopped, 4 garlic cloves, finely chopped, and one 1″ piece ginger, peeled, finely chopped, and cook, stirring occasionally, until onion is softened and deep brown in spots, 10–12 minutes.
Step 3
Add reserved sauce and ¼ cup room-temperature water to pan. Reduce heat to medium and cook, stirring often, until mixture darkens slightly, about 3 minutes. Add 1 lb. ground beef and ½ cup room-temperature water and cook, stirring often to break up meat, until water is almost completely evaporated and beef is cooked through, 8–12 minutes; remove pan from heat.
Step 4
Meanwhile, cook 12 oz. green beans, trimmed, cut into 2″ pieces, in a medium pot of boiling generously salted water until barely tender, about 5 minutes. Add 1 cup frozen peas and drain immediately. Transfer vegetables to pan with meat mixture and mix to combine. Taste and season with kosher salt if needed.
Step 5
Serve beef and green beans over steamed rice, topped with fried eggs.
