In a 3-quart stainless steel pot, combine the milk, brown sugar, white sugar, salt, and chopped dark chocolate.

Place the pot over medium heat and stir constantly with a fork until the chocolate has melted and the mixture is smooth. Continue stirring until the mixture starts bubbling, which will take about 6 minutes, then stop stirring.

Using a pastry brush dipped in water, wipe down the sides of the pot to remove any sugar crystals or chocolate splashes. Repeat this process as needed to keep the sides clean.

Attach a digital thermometer to the pot and allow the mixture to cook undisturbed until it reaches 236°F, which should take about 6 minutes. The syrup will bubble actively but stay contained in a 3-quart pot.

Once the syrup reaches 236°F, remove the pot from heat and allow the mixture to cool undisturbed until it reaches 115°F, which will take approximately 1 hour. It’s normal for small chocolate flecks to form on the sides of the pot during cooling.

Transfer the cooled syrup to the bowl of a stand mixer equipped with a paddle attachment.

Add the vanilla extract and mix on low speed until it’s evenly incorporated. Gradually increase the speed to medium and continue mixing for about 10 minutes until the mixture becomes thick and creamy.

Reduce the mixer speed to medium-low and continue beating for another 5 minutes, or until the frosting cools to 78°F.

With the mixer running, add the softened butter one tablespoon at a time, ensuring that each piece is fully blended before adding the next.

Once all the butter has been added, scrape down the sides of the bowl with a spatula. Cover the frosting and let it rest at room temperature for about 30 minutes to allow the texture to set. For optimal results, you can let it rest for up to 12 hours before using.