Make sure the butter is completely at room temperature before beginning. It can't be too cold or too warm or the buttercream won't form properly.
Melt chocolate in the microwave in 30-second increments until totally melted. Set aside.
Whip the butter on medium-high speed for a full 5 minutes. I like to pause every 90 seconds or so to scrape down the sides of the bowl.
Slowly add the condensed milk, drizzling in while it whips. It's important not to rush this step or the buttercream might split - go slowly and gradually. If you are using an electric whisk and can't drizzle and whip simultaneously, add the condensed milk in thirds, whisking until fully incorporated in between each addition.
Once all the condensed milk is incorporated, turn the mixer up to max speed for 1 minute.
Scrape down the sides of the bowl and pour in the melted chocolate, vanilla, and a pinch of salt - continue to whip until incorporated.
The buttercream should thick and glossy - if it isn't, see the troubleshooting guide in my Russian Buttercream post.
Notes
It is super important that the butter is not too cold and not too warm to make this frosting. If it's too cold the frosting won't emulsify and will look curdled, and if it's too warm it will go soupy. If this happens you can still save the frosting, see the troubleshooting guide above.I find the best results when I take my butter out of the fridge about an hour to an hour and a half before making the frosting.