Cook first 4 ingredients in a medium saucepan over medium-low heat, stirring often, 3 to 4 minutes or until cranberries begin to pop.
Whisk together cornstarch and 1 Tbsp. cold water until smooth; add to cranberry mixture, and cook, stirring constantly, 1 minute. Stir in strawberries and butter until butter is melted. Cool to room temperature (about 30 minutes). Cover and chill 6 hours.
