In a small microwave-safe bowl, heat chocolate on high in 30-second intervals, stirring between each, until melted and smooth. Stir in oil. Spread chocolate mixture into a thin, even layer on bottom of an 18x13-inch baking sheet, leaving about a 2-inch border on all sides. Freeze until hardened enough to curl when scraped, 4 to 5 minutes, checking every minute and testing corner with a small metal spatula.

Working along one long side and using a small metal spatula, scrape chocolate into curls. (If chocolate gets too soft, freeze for about 1 minute; if chocolate is too cold and breaking when scraped, let stand at room temperature for about 1 minute.) Freeze curls until ready to use.