Combine coconut milk, ginger and Thai chili in a small saucepan. Cook over low heat stirring occasionally, until bubbling around edges (10-15 minutes). Remove from heat. Let stand at room temperature, uncovered, 2-6 hours, or let come to room temperature and refrigerate overnight. Reheat coconut mixture over low heat, stirring occasionally, until thin and pourable (3-5 minutes). Pour through a strainer into a bowl. Discard solids.
Lightly grease an 8-inch square baking dish with coconut oil. Line with parchment paper, allowing at least 2 inches of overhang on all sides. Lightly grease parchment paper, and set aside.
Return infused coconut milk to saucepan. Add coconut oil, salt and vanilla. Keep warm over low heat until ready to use, stirring occasionally to mix melted oil.
Cook sugar and corn syrup in a large high-sided saucepan over medium heat, swirling the pan often, until the mixture is dark amber, (16-20 minutes). Remove from heat. Carefully add coconut milk mixture, whisking constantly until a candy thermometer registers 248℉ (firm ball stage), 4-8 minutes. Immediately pour the mixture into a prepared baking dish. Let cool, uncovered, at room temperature, for at least 8 hours or overnight.
Using parchment paper overhang as handles, lift the caramel sheet from the baking dish; discard the parchment paper. using kitchen shears, cut the caramel sheet into 15 (1/2-inch wide) rows. Cut each row into 6 (2 inch long) pieces to yield 90 caramels (minus the ones you eat). Center 1 caramel along 1 long edge of parchment paper. Roll to wrap caramel. Twist ends to seal. Repeat with remaining caramels and parchment paper.