For the cookies, cream sugars and butter until smooth. Add oil, eggs, vanilla, salt and baking soda. Mix until combined. Mix in flour.
Scoop out 1 tablespoon of dough at a time, roll into 1-inch (2.5 cm) balls and place balls on baking sheets lined with parchment paper. Press down with the bottom of a glass dipped in sugar. If the dough is too soft to form balls, chill in refrigerator for 1 hour and then roll balls.
Bake at 350°F (175°C) for 10 minutes, until cookies just begin to brown. Cool on baking sheet for 2 minutes, and then transfer cookies to wire racks to cool completely.
For the frosting, beat the butter and powdered sugar* together. Add the vanilla extract. Gradually add milk and beat until you have reached a creamy consistency. Spread on the cooled cookies and top with sprinkles or colored sugar if desired. Let the frosting set for a few hours before stacking the cookies.
Store in an airtight container at room temperature for up to one week.
Notes
This is my sister-in-law's recipe that she passed on to me. It is a photocopy of a hand-typed recipe. If anyone can tell me the original author of this recipe, I would be happy to update this and give credit where credit is due! One of the best cookie recipes you will ever find!