Start by browning ALL of your butter at once. Add 9 tablespoons of unsalted butter to a light colored saucepan over medium heat. Let it melt, then keep swirling the pan as it foams and bubbles. After about 5 to 7 minutes the milk solids at the bottom will turn golden brown and it will smell like toasted nuts. Pull it off the heat immediately and scrape everything, browned bits included, into a bowl to cool slightly. You should have about 7 tablespoons. Measure out 3 tablespoons for the dough, 1 tablespoon for the cream cheese filling, and 3 tablespoons for the crumble.
Heat 3/4 cup of whole milk to between 100 and 110 degrees F. I really do use a thermometer here, because this is the one step where guessing can cost you your whole rise. It should feel warm on your wrist, never hot.
Stir in the 2 teaspoons of active dry yeast and let it sit for 5 to 10 minutes. You are looking for it to get foamy and bubbly on top, which means your yeast is alive and happy.
Mix in the light brown sugar, the egg, and 3 tablespoons of your brown butter until combined. Then add the bread flour, cinnamon, and salt.
Knead for 8 to 10 minutes, until the dough is smooth, elastic, and just slightly tacky. It should pull away from the sides of the bowl and spring back when you poke it.
Cover the bowl and let the dough rise for 1 hour, until doubled and beautifully puffy. Now is the perfect time to make everything else!
Make the apple pie filling. Peel and dice 2 apples nice and small. Melt 1 tablespoon of butter in a skillet over medium heat, add the apples, 2 tablespoons of light brown sugar, and 1/2 teaspoon of cinnamon. Cook for 6 to 8 minutes, until the apples are tender and syrupy. Sprinkle in the cornstarch, stir, and cook 1 more minute until glossy and thick. Set aside to cool completely.
Make the brown butter cream cheese filling. Beat the room temperature cream cheese with 1 tablespoon of brown butter, 1 tablespoon of heavy cream, and 1 teaspoon of vanilla until totally smooth. Then add the powdered sugar SLOWLY, a little at a time, beating until light and fluffy. Transfer it to a piping bag, or just grab a spoon.
Make the salted crumble. Whisk together 3 tablespoons of brown butter, the all purpose flour, light brown sugar, vanilla, cinnamon, and flaky sea salt until it comes together in big crumbly clumps. Do not overwork it, those craggy clumps are exactly what you want.
Once the dough has risen, punch it down and divide it into 6 equal balls, about 100 grams each. A kitchen scale makes this easy, but eyeballing it is fine too. Place them on a parchment lined sheet pan with plenty of room between them since they spread.
Press down into the center of each ball with your fingers to create a well, leaving a nice puffy border. Brush that border generously with egg wash.
Now we layer! Pipe the cream cheese filling into each well, add a drizzle of salted caramel right on top, spoon on the apple pie filling, and finish with a big pile of that brown butter crumble.
Bake at 375 degrees F for 20 to 22 minutes, until the buns are GOLDEN and your kitchen smells like the best fall candle that has ever existed.
Let them cool for about 10 minutes, then drizzle with extra salted caramel and finish with a sprinkle of flaky sea salt. Serve them warm and get ready for everyone to lose their minds!