Preheat oven to 350℉. Line a 9x13 baking dish with parchment paper with enough to leave extra hanging over the sides (your going to use the parchment to lift the shortbread out of the dish later).
Combine the flour, cornstarch and salt in a small bowl. Mix well with a fork to distribute the cornstarch evenly throughout the flour.
In a stand mixer, mix the butter at medium speed for 2 minutes until it gets lighter in color and a little fluffy. Scrape down the sides. Add the oil and beat on medium speed for 3 minutes until well combined, stopping to scrape down the sides at least once. Gradually add the sugar, beating well. Add the vanilla bean paste or seeds and mix to distribute. Scrape down the sides of the bowl.
Add the flour mixture all at once. Beat at low speed just until combined. Stop and scrape the sides one more time and mix on low again just to ensure all flour is mixed in. The mixture should be a moist and crumbly dough.
Transfer the dough to the baking dish, spreading as evenly as possible. Lay a second piece of parchment over the top of the dough and use your palm to press down lightly on the dough until it is packed into the dish and spread evenly to all sides and corners. Peel the parchment back. If you see lots of cracks, replace the parchment and keep smoothing until it looks homogenous.
Bake for 20-25 minutes. Starting checking at 18 minutes. If you see any signs of browning on the edges, remove from oven. The shortbread should look dry but not crispy or golden. My picture looks more golden than it is due to the oven light. The color should not look much different than it did when it went in the oven.
Allow to rest for about 10 minutes in the dish. Cut the shortbread into squares (about 3" by 3"). Use a sharp knife or a flat edged food scraper. Be gentle. Once the shortbread is cut, carefully lift it out of the baking dish using the parchment paper as your handles. Set on a flat surface and allow to cool completely. Carefully transfer to an airtight container, using parchment paper between layers if needed. Eat within a week for best freshness.