Preheat the oven to 300°F. Lightly grease 2 round 9" baking pans. If you are worried that the cookies might stick to the bottom, then line the bottom with parchment paper and grease the parchment. I don't have 9" round pans, so I used one 9" square pan and one 6" round pan instead.
In a medium sized mixing bowl, beat together butter, sugar and vanilla extract until light and fluffy. Then add flour and pecans (toasted and chopped) and beat until the mixture comes together. Initially it will look as if the dough is never going to come together, but after 30 seconds of continuous beating, it will come together. If it absolutely doesn't come together, then dribble in 1tablespoon water, until it does. This is a stiff dough.
Divide the dough between the 2 baking pans and then smoothen the top with your fingers.
Prick the surface with a fork all over to let the steam escape.
Bake until the shortbread is light golden on the top surface and a deeper golden brown around the edges, about 35 minutes.
Remove from the oven and immediately turn it out onto a clean working surface.
When still warm, using a pizza wheel or a sharp knife, cut the shortbread into wedges or rectangles. If you wait till the shortbread cools, then it will be difficult to cut the cookies.
Place the cookies on a wire rack to cool completely.