In a separate bowl, beat the butter and sugars together for about 2-3 minutes with an electric mixer. Add the vanilla and the eggs and beat for another 2-3 minutes.
Add the flour mixture to the butter mixture and mix just until combined.
Use a cookie scoop to scoop out a tablespoon of dough and shape it into a ball. Flatten it out and place a Rolo in the center. Wrap the dough around the Rolo and roll in your hands to form a ball that completely covers the candy.
Place the cookie dough balls about 2" apart on a greased cookie sheet or a cookie sheet lined with parchment paper or a silicone baking mat. Bake for 8-10 minutes or until the tops barely begin to turn a light golden brown. The tops should be slightly cracked.
Notes
NOTE: If you would like to make chocolate cookies instead of regular ones, you can use 2 3/4 cups of flour and 3/4 cup cocoa instead of the 3 1/2 cups of flour. We love this version too!