Preheat oven to 350°F (175°C). Line a 12-cup muffin pan with liners.
Brown the butter: In a saucepan, melt cold butter over medium heat until golden brown and nutty in aroma. Stir frequently. Remove from heat and mix in the split vanilla bean seeds. Let cool slightly.
In a large bowl, whisk together cake flour, sugar, baking powder, and sea salt.
In another bowl, combine browned butter (90g), canola oil, vanilla extract, eggs, and buttermilk. Mix well.
Gradually add wet ingredients to dry, stirring just until combined. Do not overmix.
Divide batter evenly into muffin cups and bake for 16-18 minutes or until a toothpick comes out clean. Let cupcakes cool completely.
For the buttercream, whip remaining browned butter with cream cheese, vanilla extract, and salt until smooth. Gradually add powdered sugar until fluffy.
Frost cooled cupcakes with brown butter buttercream and enjoy!