In a bowl, whisk together 1/4 cup low-sodium soy sauce, 1/4 cup brown sugar, 2 tablespoons rice vinegar, 1 tablespoon cornstarch, 1 tablespoon grated fresh ginger, 4 cloves finely minced garlic, and 1 teaspoon chili garlic sauce (use more or less to taste) until the cornstarch is fully dissolved and the mixture is smooth. Set the sauce aside.

Heat a large non-stick skillet over medium-high heat until hot. Add 1 tablespoon olive oil.

Add the 1 pound large shrimp (shells removed) in a single layer. Cook about 1–2 minutes per side, until the shrimp are pink and opaque. Transfer the cooked shrimp to a plate and set aside.

Return the skillet to medium-high heat and add the remaining 1 tablespoon olive oil. Add the thinly sliced onion and sauté, stirring occasionally, about 5 minutes, until the onion is softened and starting to turn golden.

Add the 3 cups broccoli florets to the skillet. Cook, stirring often, until the broccoli is bright green and crisp-tender, about 7 minutes.

Return the cooked shrimp to the skillet. Pour the prepared sauce over the shrimp, onion, and broccoli. Stir and bring to a simmer, cooking until the sauce thickens and everything is evenly coated, about 1–2 minutes.

Remove from heat and serve immediately.