Pound lemon grass with a meat mallet to slightly flatten and break apart fibers.
Combine lemon grass, vinegar, and next 9 ingredients in a small saucepan; bring to a boil over medium-high heat. Reduce heat and simmer, uncovered, 35 minutes, stirring occasionally.
Pour mixture through a fine wire-mesh strainer into a bowl, using the back of a spoon to press out juice. Discard solids. Return juice to pan.
Whisk 1 tablespoon water into cornstarch in a small bowl until smooth. Whisk into sauce. Bring to a boil over medium-high heat, whisking constantly. Boil, whisking constantly, 1 minute or until thickened.