Preheat the oven to 350°F. Sift the flour and salt into a medium bowl. Beat the butter and sugar with an electric mixer on medium speed in a large bowl until just combined; add the vanilla. With the mixer on low speed, add the flour mixture to the butter and sugar and mix just until the dough starts to come together.
Put the egg wash and coconut in two separate medium bowls. Form 1¼-inch balls of dough (about 1 tablespoon each); dip each ball in egg wash, then roll in coconut. Place the balls about 2 inches apart on a cookie sheet; press a light indentation into the top of each with your finger. Bake until the coconut is golden, 18 to 20 minutes. Remove the cookies from the oven and press the back of a teaspoon in the center of each to re-form the indentations. Transfer to a rack to cool.
Place the chocolate chips in a medium glass bowl. Bring the cream just to a boil in a small saucepan over medium-high heat, pour over the chocolate chips and let sit for 2 minutes, then stir until the cream is fully incorporated and the mixture is smooth.
Spoon ½ teaspoon of chocolate into the center of each cookie and let set for 5 minutes. Top each cookie with 3 chocolate eggs.
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