Line a large baking sheet with parchment and clear space in the fridge.
Beat condensed milk, butter, corn syrup, peppermint, vanilla, and salt until smooth and creamy.
Mix in powdered sugar gradually, then knead briefly until a soft, non-sticky dough forms.
Scoop 1-tbsp portions, roll into balls, and flatten into 1/4-inch disks on the prepared sheet.
Chill the peppermint disks until firm, about 20 minutes.
Melt chocolate with coconut oil in 30-second microwave bursts, stirring until glossy and smooth.
Dip each peppermint disk in chocolate, let excess drip off, and return to the sheet.
Chill until the chocolate sets, about 10 minutes, then serve or store.