Preheat the oven to 300ºF and grease two round 9-inch cake pans with butter. (If the pans are not non-stick, line them with greased parchment paper).
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter, sugar and vanilla until light and fluffy, about 3 minutes. Add the flour, 1 cup at a time, mixing just until combined.
Divide the dough evenly between the two greased pans and press it into an even layer. Using a fork, prick the dough all over.
Bake for 35 minutes, or until the shortbread is pale golden in the center and slightly darker around the edges.
Remove the shortbread from the oven and immediately invert the pans onto a cutting board. (If the shortbread won't release from the pan, use a sharp knife to cut around the edges.) Using a sharp knife, immediately cut each shortbread round into 8 wedges. It is important to cut the shortbread while it's still warm, otherwise it will crumble if you try to cut it after it has cooled.
Transfer the shortbread wedges to a cooling rack to cool completely.
Melt the candy melts with the vegetable oil in a microwave or double-boiler, stirring until smooth. Transfer the mixture to a piping bag or plastic bag, snip off the tip of the bag and then drizzle it onto the cookies.
Immediately top the cookies with sprinkles and serve.
If you can't find green candy melts, you can use any variety of chocolate. White chocolate would be a beautiful snowy addition to the buttery shortbread trees.