Preheat the oven to 350°F. Line a 9x13-inch baking pan with parchment paper.
To make the batter: In the bowl of a stand mixer with the paddle attachment, add the canola oil, buttermilk, eggs, and cane sugar. Mix together until the eggs are completely combined.
Add the cake flour, ground vanilla bean, baking powder, and salt. Mix on low until combined into a smooth cake batter.
Transfer the batter to the prepared baking pan and spread it out evenly.
Bake for 28 to 33 minutes, or until a toothpick inserted in the center comes out clean. Allow the cake to cool completely in the baking pan.
To make the icing: In the bowl of a stand mixer fitted with the paddle attachment (or using a hand mixer) add the butter, powdered sugar, heavy cream and vanilla extract.
Mix on low until combined, and then speed mixer up to high and mix for 2 to 3 minutes. Be sure to scrape down the sides of the bowl part way through mixing to ensure everything is mixed and smooth.
Add the icing to the cooled cake and spread it out evenly. I like to top with a little bit of naturally colored white sprinkles, but this is optional!
Store in an airtight container in the fridge for up to 3 days.