To brown the Butter:

1. In a heavy saucepan, medium-low heat, melt the butter.
2. Continue cooking the butter until it begins to bubble.
3. Using a whisk, stir and swirl the butter continuously to keep the solids from sticking to the bottom. Initially, you will see large-sized bubbles, and then as it continues to cook off the water in the butter, the bubbles will become smaller in size. Then, at the point, it begins to FOAM, keep swirling the butter until the milk solids have reached a golden brown color. Remove from the heat and swish the butter in the pan.
4. Set butter aside, and let it come to room temperature.

Make the Shortbread Cookies:

1. Preheat the oven to 350 F.
2. Transfer the butter into a bowl, and add the flour, cornstarch, sugar, and vanilla. Mix the ingredients together using an electric mixer on low speed until the ingredients are combined.
3. Line an 8 x 8 baking pan with parchment paper (or grease it). Transfer the dough to the pan and press the dough into the pan.
4. Bake for approximately 25 – 30 minutes or until the edges begin to brown.
5. Remove from the oven and let completely cool before cutting into squares and serving.