With the rack in the center, heat the oven to 350°. Line two baking sheets with parchment paper. In a medium bowl, whisk the eggs until they're frothy, about 1 minute. With a wooden spoon, stir in the condensed milk, corn syrup, salt, and vanilla extract until blended. Stir in the coconut until evenly mixed.
With wet hands, roll heaping teaspoons of the coconut mixture into balls, pressing them to make them compact. Place them on the baking sheets, 1 1/2 inches apart. Shape each ball into a pyramid.
Bake the cookies until their edges are golden brown, about 15 minutes. Take care not to overbake them, they'll be too hard once cooled. Set the baking sheets on a cooling rack for a few minutes, then transfer the cookies directly to the rack to cool completely.
Line a baking sheet with parchment or waxed paper. tip: The cookies will need to chill, so choose a pan or pans to fit your refrigerator space. Place the chocolate in a medium bowl, then set the bowl over a pan of simmering water. Do not let the bottom of the bowl touch the water. Let the chocolate melt, stirring occasionally, until smooth. Remove the pan from the heat and stir in the vegetable oil.
Dip the bottom of each macaroon in the chocolate, gently shake off the excess, and set it on the prepared baking sheet. Chill the cookies in the refrigerator until the chocolate is set, about 25 minutes. You can store the cookies, layered between sheets of parchment or waxed paper, in an airtight container for up to five days.