In a medium bowl, combine the brown butter with the egg yolks. Whisk until well combined.
Meanwhile, add the heavy cream, salt, and coffee into a saucepan on low heat. Mix and continue stirring until it thickens. You want it to heat until it just simmers – don’t let it simmer and bubble.
Start slowly pouring the hot mixture into the egg and butter mixture (from step 1) while mixing (it should be well combined).
Transfer the mixture to a saucepan (you can use the same one from step 2), and heat on medium-low until it thickens (but don’t let it simmer). Continue mixing until it coats the spoon (it should take about 10-15 minutes).
Turn off the heat and add the vanilla. Mix well. Then, place a mesh strainer into a large bowl. Pour the ice cream base through.
Allow it to cool for 15 minutes and then cover and refrigerate overnight.
Pour the ice cream base into the ice cream maker and turn it on according to your ice cream maker instructions. Enjoy!