Place the butter into a small saucepan over medium heat. Cook the butter until deep golden brown, and the butter stops popping. Set aside to cool until warm.
¼ cup unsalted butter
In a medium saucepan over medium-low heat, combine the milk, ¼ cup of brown sugar and salt and bring to a simmer.
2 cups whole milk, ½ cup light brown sugar, packed, divided, ⅛ teaspoon fine sea salt
Meanwhile, in a large bowl, combine the remaining ¼ cup of sugar and egg yolks and whisk until fully mixed, about 30 seconds.
5 large egg yolks
Whisk in the cornstarch until thickened, for about a minute.
3 tablespoons cornstarch
When the milk mixture is simmering, remove the saucepan from the heat. Carefully and slowly, whisk the milk into the egg mixture.
Pour the egg/milk mixture back into the saucepan and place over medium heat, whisking continuously until the pastry cream thickens and slow bubbles pop on the surface.
Whisk in the brown butter and vanilla bean paste.
2 teaspoons pure vanilla paste (or vanilla extract)
Strain the mixture through a fine mesh sieve into a clean bowl to remove any curdled bits, and to smooth out the cream.
Cover the surface of the pastry cream with plastic wrap so that a skin doesn't form. Allow the pastry cream to cool to room temperature.
Chill the pastry cream in the fridge until completely chilled, about 3 hours, preferably overnight before using.