Start the rice and rice water in a covered saucepan; simmer on low for 15 minutes after boiling, then rest for 5 minutes.
Heat 1 tablespoon oil in a large skillet over medium-high heat. Add the eggplant and brown for 4 minutes, then add 1/2 cup water, cover and cook for 4 minutes until nearly tender; transfer to a bowl.
Add the remaining oil and beef to the skillet. Brown for 5 to 6 minutes, breaking it into crumbles and cooking to 160°F.
Stir in garlic, ginger and chili bean paste for 30 seconds. Add broth, soy sauce and the eggplant; simmer for 2 minutes.
Mix cornstarch with 1 tablespoon cold water and stir into the bubbling sauce. Cook for 1 minute until lightly thickened, fold in scallions and serve over rice.