In a heavy saucepan combine egg whites, sugar and coconut flakes and cook over medium-low heat, stirring frequently until all the ingredients combine together, about 12 minutes. The mixture should be sticky and moist, not dry.
Remove from heat and stir in the almond and vanilla extracts.
Set aside and let it cool 10 minutes, should be warm.
Preheat the oven to 300°F. Spray a nonstick a mini muffin tin with oil.
Drop heaping tablespoons into the tin, lightly press mixture into the bottom and up the sides of the tin to make "nests" with the back of the measuring spoon.
Bake 22 to 25 minutes, or until golden.
Let it cool 10 minutes, then carefully remove from the tin.
Arrange the nests and top each with two mini chocolate eggs.