Begin by preheating your oven to 350 degrees F.
In a large bowl, beat together your butter and sugar with a mixer on medium speed until light and fluffy (about 3 minutes); then beat in the vanilla and salt. With the mixer on low, gradually add the flour and beat until just combined.
Roll the dough with your hands into 1-inch balls.
Then, in one small bowl place your lightly beaten eggs. In another small bowl, place your coconut. Dip each ball first in the egg, then roll in the coconut.
Place balls on a parchment-lined baking sheet. Press an indentation into each ball with your thumb, finger, or back of a wooden spoon. Bake for 10 minutes. Remove the cookies from the oven and re-press the indentations. (Use caution since the cookies are hot.) Place the cookies back in the oven for an additional 10 minutes or until the cookies and coconut are golden.
Remove and let cool on a wire rack.
Now, place the unwrapped caramels and heavy cream in a sauce pan over low heat. Stir constantly until the caramels are melted and the mixture is smooth. Spoon the caramel sauce into the cookie indentations. Then, sprinkle with sea salt.