Let's cook.
In a medium non-stick saucepan, combine the sweetened condensed milk, 2 cups of shredded coconut, and butter. Stir well to combine.
Cook over medium-low heat, stirring constantly with a silicone spatula, for about 8-10 minutes. The mixture will thicken and start to pull away from the sides and bottom of the pan, resembling a soft dough.
Remove the saucepan from the heat and stir in the vanilla extract. Transfer the mixture to a shallow dish or plate and let it cool completely at room temperature, about 30-45 minutes. This makes it easier to handle.
Once cooled, lightly grease your hands with a tiny bit of butter or cooking spray. Take about 1 tablespoon of the coconut mixture and roll it into a small ball, roughly 1 inch in diameter.
Place extra shredded coconut in a separate shallow dish. Roll each coconut ball in the shredded coconut until fully coated.
Arrange the coated coconut balls on a serving platter or in mini paper cupcake liners.
If desired, gently press one whole clove into the top of each cookie for a traditional garnish.
Serve immediately or store for later enjoyment.
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