Add 10 tbsp unsalted butter to a light-colored saucepan and cook over medium heat, stirring often, until the butter foams, then the milk solids turn golden brown and smell nutty, 5–7 minutes; immediately pour into a heatproof bowl, scraping in all the browned bits.
Chill the brown butter in the refrigerator, stirring every few minutes, until opaque and spreadable but not firm, about 15–20 minutes.
Preheat the oven to 350°F and line a 12-cup muffin pan with paper liners.
In a medium bowl, whisk together the all-purpose flour, baking powder, baking soda, and fine sea salt.
In a large mixing bowl, combine the granulated sugar and light brown sugar, then add 90 g (about 6 1/2 tbsp) of the spreadable brown butter and the neutral oil; beat on medium speed until the mixture looks sandy and well combined, 1–2 minutes, scraping down the bowl.
Add the flour mixture to the butter mixture and mix on low speed until the flour is evenly coated and the mixture resembles damp sand.
In a separate bowl or large measuring cup, whisk together the eggs, egg yolk, buttermilk, vanilla bean paste, and vanilla bean seeds (or vanilla bean paste) until smooth.
Add half of the wet mixture to the flour mixture and beat on low speed until just combined, scraping down the bowl; add the remaining wet mixture and beat until the batter is smooth and thick but pourable.
Use a cookie scoop or spoon to divide the batter evenly among the 12 lined muffin cups, filling each about two-thirds full.
Bake for 18–20 minutes, or until the cupcakes are lightly golden and a toothpick inserted in the center comes out with a few moist crumbs.
Let the cupcakes cool in the pan for 5 minutes, then transfer to a wire rack to cool completely before frosting.
While the cupcakes cool, add the remaining brown butter (about 3 1/2 tbsp) to a mixing bowl with the softened cream cheese and beat on medium speed until smooth and creamy.
Add the powdered sugar, vanilla bean paste, and pinch of salt to the brown butter–cream cheese mixture; beat on low speed until incorporated, then increase to medium and beat until fluffy, 1–2 minutes.
Add heavy cream or milk, 1 tbsp at a time, beating until the frosting is smooth, light, and spreadable.
Once the cupcakes are completely cool, frost the tops generously with the brown butter cream cheese frosting using a spatula or piping bag.
Serve immediately, or store frosted cupcakes in an airtight container at room temperature for 1 day or refrigerated for up to 4 days; bring refrigerated cupcakes to room temperature before serving.