Preheat oven to 350°F.
Cream butter and sugar together until light and fluffy. Add vanilla and slowly add flour and mix until just combined. Fold in chopped pecans, beating at low speed, scraping bowl as necessary, until well mixed.
Roll dough into little balls. Place on prepared cookie sheet about 2 inches apart. Chilling the dough for 30 minutes in the fridge helps the cookies stay round but we are never that patient!
Bake cookies for 14 - 15 minutes until bottoms are just slightly brown.
Remove from oven and cool on cooling rack until you can handle them comfortably with your hands.
While cookies are still warm, roll them in icing sugar. Place cookies on cooling rack, once they have cooled completely, roll them in icing sugar again.
Store cookies in an airtight container for up to 3 days or freeze for up to one month.