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1
Put 1/4 cup of unsalted butter in a heavy-bottomed saucepan and set over medium heat. Watch carefully as it browns, swirling the pan continuously. It will melt, and start to look like it is separating. Next, it will begin to foam up. Continue watching closely and swirling the pan regularly until the milk solids begin to turn brown and smell nutty and caramel-y. When the butter is sufficiently browned, and has made your entire house smell like a dream, pour it into a bowl and set aside to cool. Make sure you get all the scrumpy browny bits off the bottom of the pan: they are the best part.
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2
Make an ice-water bath in a large bowl. In a medium bowl that will fit comfortably inside the large one, mix half-and-half, white sugar, and eggs. Set aside.
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3
In a saucepan over medium heat, mix heavy cream and brown sugar. When mixture is hot and just starting to bubble at the edges, remove from heat, and slowly pour into half-and-half mixture while whisking constantly. Return mixture to the saucepan, and rinse and dry the now-empty medium-sized bowl. Place a fine sieve inside it, and set it aside.
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4
Place the saucepan back over medium heat and cook, stirring constantly, until the custard reaches 170u00b0F. If you do not have a thermometer, heat until the mixture is thickened, and coats the back of your spoon or spatula rather than simply running off.
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5
Pour the thickened custard through the sieve and into the bowl. Set the bowl in the ice water bath, and whisk in the vanilla, and 4 tbsp of the browned butter. As I said before, make sure you get plenty of the scrumpy brown bits. (Depending on the water content of the original 1/4 cup of butter, you may have some browned butter left over. This is a horrible affliction you may have to deal with by using it to fry eggs, dipping bread in it, or adding it to cauliflower soup. I trust that you will be able to bear this burden in a multitude of delicious ways.)
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6
Leave the custard in the ice-water bath until entirely cool. If your kitchen is particularly warm, or you want to speed-up the process, you can transfer the entire ice-water bath contraption to your fridge.
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7
When the custard is completely cooled, churn in your ice cream maker according to its directions. About a minute before it is done churning, add the chopped chocolate. When done, scrape into a freezer-safe container and freeze for several hours.
