Step 1

Separate broccoli stem from crown. Remove any leaves from stem; thinly slice leaves. Slice stem into ½"-thick coins; cut crown into 1" florets.

Step 2

Separate dark green tops from scallions and cut into 1" lengths. Thinly slice white and pale green scallion parts. Keep separate.

Step 3

Squeeze 1 cup kimchi over a small bowl to expel as much liquid as possible. Coarsely chop kimchi; return liquid to kimchi jar.

Step 4

Heat 1 Tbsp. vegetable oil in a large wok or nonstick skillet over medium-high. Add broccoli and dark green scallion parts, season with salt, and cook, undisturbed, until beginning to char, about 5 minutes. Stir and cook another minute; transfer to a plate.

Step 5

Add 1 Tbsp. vegetable oil to same pan. Cook kimchi, white and pale green scallion parts, garlic, and ginger, stirring often, until softened and fragrant, about 2 minutes; push aromatics to edges of pan. Drizzle remaining 1 Tbsp. vegetable oil into empty space and add rice, sesame oil, and ¼ cup soy sauce. Toss rice and aromatics together, then press into an even layer and cook, undisturbed, until slightly crisped underneath, about 5 minutes.

Step 6

Return broccoli and scallion tops to pan and cook, tossing often, until rice and vegetables are heated through, about 2 minutes. Season with salt.

Step 7

Divide fried rice among plates and top each with a fried egg, some sesame seeds, and more kimchi; season with pepper. Season eggs with a dash of soy sauce.