What is this dipped powder cookie called?
Found it!
The recipe was in a book at my house called Cookies and published by Reader's Digest (ISBN: 0-7621-0593-3).
This recipe is typed up verbatim from the source mentioned above.

Two-Tone Cookies
1 2/3 cups all-purpose flour
1 teaspoon baking powder
1/8 teaspoon salt
1/3 cup butter, softened
1/4 cup granulated sugar
2 large eggs
1 tablespoon milk
1/4 cup confectioners' sugar
1/4 cup unsweetened cocoa powder
Preheat the oven to 350°F. Butter two cookie sheets. Sift the flour, baking powder, and salt into a large bowl and make a well in the center. Add the butter, sugar, eggs, and milk. Use your hands to knead the mixture into a smooth dough. Form the dough into balls the size of walnuts and place 1 inch apart on the prepared cookie sheets. Bake for 15-20 minutes, or until just golden, rotating the sheets halfway through for even baking. Transfer to racks and let cool completely. Dip half of each cookie in the confectioners' sugar and the remaining half in the cocoa.
Makes 26 cookies. Prep: 35 min. Cooking: 15-20 min. Level: 1. Keeps 5 days.

I made the cookies a couple nights ago- they are a bit time-consuming to bake and dip, but I ended up with the cookies that I remembered- light and covered half with cocoa powder and half with confectioners' sugar. I used little bowls of powder to dip the cookies in. Here is a picture that I took of the finished cookie:

In terms of eating them, I recommend eating the entire cookie in one bite. If you decide to have a little nibble, you won't really enjoy the whole mixture of the flavors of the cocoa and the sugar at once :) Enjoy.