Preheat oven to 350°. Line a large cookie sheet with parchment paper and set aside.
In a medium mixing bowl, add the flour, baking powder and salt. Whisk to combine. Set aside.
In a large mixing bowl, cream together the butter and 1 cup of sugar. Add the egg and vanilla extract and mix until incorporated.
Add half of the dry ingredients to the wet ingredients and mix until well combined. Add the remaining flour mixture and mix well.
Cover and chill the dough for 15 minutes for easier handling.
Pour 1/3 cup of sugar into a shallow bowl. Shape the chilled cookie dough into 1 inch balls and roll in the granulated sugar.
Place the sugar-coated cookie dough balls on the lined cookie sheet, about 2 inches apart. (The dough will not expand much as this recipe was adapted from a thumbprint cookie recipe).
Bake for 8-10 minutes or until the edges start to turn golden brown.
Allow to cool on cookie sheet for 3 minutes before transferring to a wire rack to completely cool.
While the cookies are cooling, line a cookie sheet with parchment paper and set aside. Combine the powdered sugar and milk in a small mixing bowl. Stir until a think glaze forms.
Dip the tops of each cookie into the glaze and place back on the lined cookie sheet.
Sprinkle with the rainbow nonpareil's and place one jellybean on top of each cookie.