In a large bowl, stir together the sweetened condensed milk, shredded coconut, and vanilla until evenly combined and very sticky.

Drop heaped tablespoonfuls onto a parchment-lined baking sheet, flatten slightly, and refrigerate until firm, about 30 minutes.

Melt the chocolate chips and oil together in the microwave, drizzle over the chilled cookies, let set for a few minutes, then serve.