In a large sauté pan, combine the sugar and corn syrup. Cook over medium heat until lightly caramelized. (Do not stir; gently swirl the pan.) Carefully add the verjus to dissolve the sugar, then reduce the heat to low.
Add the plum halves, cut side down, and cook on low heat for 10 minutes. Flip so they are face-up and cook for another 10 minutes, until the plums are soft but not fallin