1. In large bowl or bowl of a stand mixer, cream together butter and sugars until light and fluffy.
2. Add eggs, oil and vanilla and beat well until fluffy.
3. Sift together flour, baking soda, cream of tartar and salt, and slowly add to sugar mixture while beating. Mix until well combined.
4. Refrigerate dough for at least 30 minutes, or until it is firm enough to press or roll out.
5. When you're ready to bake, preheat the oven to 350°F.
6. If you're going to roll the dough, roll it onto a sheet of parchment, then chill again before using cookie cutters to cut the shapes out. I find it easier to take a small piece of dough (the size of one cookie) and flatten it out directly onto the baking sheet. Then use the cookie cutter to cut out a shape and remove the excess. Repeat with the rest of the dough. Either way, the colder the dough, the easier it will be to cut clean shapes.
7. Place cut out dough onto an ungreased baking sheet (you can line it with a silicone baking mat if you'd like) and bake 9-12 minutes or until cookies are slightly golden on the edges. Remove from cookie sheet onto a cooling rack to cool completely before frosting.
8. Frost and decorate cookies as desired.

For the Icing:

1. Place powdered sugar in a bowl. Add vanilla, then milk, one tbsp at a time, stirring or beating with a mixer constantly until you reach the desired consistency.
2. Add food coloring one drop at a time, if using.
3. Add frosting to a squeeze bottle or zip-top bag with the corner snipped off so that you can easily squeeze the frosting onto the cookies.
4. Frost cookies and let dry before stacking or storing them. If you use sprinkles, do so immediately after adding frosting so that they stick.