First, brown the butter: Place the butter in a skillet over medium heat. Cook as it melts, then sputters and foams. When it stops sputtering and is nearly silent, and you see brown bits at the bottom. Scrape it all, including brown bits into a heatproof bowl and set aside to cool.
To make the crust: Either in a food processor or in the bowl of a stand mixer fitted with the paddle attachment, combine the sugar and butter until blended then add remaining ingredients and pulse/mix until the dough sticks together when you press it. Press the dough into the bottom and up the sides of a 9 or 10” round tart pan with a removable bottom. Set crust in the freezer for 10-15 minutes and preheat the oven to 350 F. Cover the pan with parchment paper and fill with pie weights or dried beans. Bake for 20 minutes, then remove the beans/parchment and dock the bottom with a fork. Return to the oven for another 10-15 minutes. Let the crust completely chill before adding the filling.
To make the brown butter ganache (filling): Combine the cooled brown butter with the chocolate and set in the microwave for 30 seconds, until the butter is mostly melted and the chocolate is beginning to melt. Warm the cream in a pot until it’s bubbling on the sides, this will happen in a few minutes (careful not to overheat it!). Pour it over the chocolate & butter and mix, adding the vanilla and stirring until you have a smooth ganache. Pour into the chilled crust and set in the fridge.
To make the peanut butter mousse: In the bowl of a stand mixer, or with a hand mixer: beat the cream cheese and peanut butter together until smooth. Add the salt, sugar and vanilla and beat to combine. Pour in the heavy cream and beat until creamy and fluffy. Spread the mousse over the ganache and set in the fridge to chill, at least 2 hours before serving.