Heat a large skillet over medium heat. Add 1 pound ground beef, ½ teaspoon garlic powder, ¼ teaspoon salt, and ¼ teaspoon pepper. Cook, breaking the meat into pieces, until no longer pink.
Drain excess fat from the skillet and transfer the cooked beef to a plate; leave the pan in place.
Add 1 tablespoon olive oil to the same skillet and heat over medium-high heat until shimmering.
Add 4 cups fresh broccoli florets and 1 small onion (sliced thin) to the skillet. Cook, stirring occasionally, until the broccoli is crisp-tender, about 4–5 minutes. (If you prefer softer broccoli, cover the pan for part of the cooking time to steam it.)
While the vegetables cook, whisk together ½ cup water, ¼ cup low-sodium soy sauce, 2 tablespoons brown sugar, 1 teaspoon ground ginger, and 2 tablespoons cornstarch in a bowl until the cornstarch is fully dissolved and the mixture is smooth.
Return the cooked beef to the skillet with the broccoli and onion. Stir to combine.
Pour the soy sauce mixture into the skillet and cook, stirring constantly, until the sauce thickens and coats the beef and vegetables, about 1–2 minutes.
Remove from heat and serve immediately over hot cooked rice.