Beat the butter and sugars in a large bowl with an electric hand mixer for about 2 minutes, or until light and creamy.
Add the vanilla and eggs and beat for another minute.
In a small bowl, whisk together the flour, cocoa, baking soda, and salt. Add to the wet ingredients and stir until barely combined. Stir in about 1 1/2 cups of the white morsels. Save the rest for the tops of the cookies.
Cover the dough (or wrap it in plastic wrap) and chill for 2-3 hours.
Preheat your oven to 350° and line baking sheets with silicone liners or parchment.
Roll into tablespoon-sized balls and place at least 2 inches apart on prepared baking sheet. Bake at 350 degrees for 8-10 minutes, or until set in the middle. Immediately press a few white chips on top of each cookie.
Let cookies cool on the pan for 2-3 minutes, then use a metal spatula to transfer them to a wire rack to cool completely.
Notes
My cookie dough balls were about an ounce. If yours are smaller, decrease baking time. If they are larger, bake them longer.
Chilling the cookie dough makes for thicker cookies. If you bake them immediately, they will spread and be flat. If you are in a hurry, you can roll the dough into balls and chill them for 30-45 minutes.