Start by melting the chocolate because it needs time to cool down before it's added to the frosting. Make sure you're using high-quality chocolate bars or couvertures. Place 3/4 cup of chocolate that's been finely chopped into a microwave-safe bowl. Heat in 15-second intervals, stirring between intervals to help the chocolate melt more evenly. Once the chocolate is mostly melted (it usually takes 4 intervals for me), stir until smooth, then set aside to cool.
Next, clean your mixing bowl and whisk the attachment with a splash of lemon juice or vinegar to remove residual grease from prior baking. This helps ensure your egg whites whip up properly.
Then beat 4 large room-temperature egg whites and 1/4 tsp cream of tartar together at a medium-high speed. Slowly add 1/3 cup of granulated sugar and continue beating until soft peaks form. Stop the mixer at this point.
Then add the remaining 1 cup of sugar and 1/3 cup of water into a medium pot and place on medium-low heat. Stir until the sugar melts and becomes clear. Continue to heat the mixture at medium-high heat until the sugar reaches 240F/ 116C.
Turn the mixer back on to a medium-high speed and slowly pour the sugar into the whipped egg whites. Try to pour the syrup directly on top of the egg whites and avoid having it hit the side of your bowl. Continue to mix on medium-high until the mixture increases in volume and becomes shiny with stiff peaks. It's marshmallow frosting at this stage, which is great for s'mores-flavored treats or pies!
Then, feel the bottom of your bowl and make sure the meringue isn't still warm. If it is, let it sit for a few minutes to cool. If it is, I like to place bags of frozen veggies around the base to help it cool.
Switch the whisk to the paddle attachment, turn the mixer onto medium speed, and add 2 cups of room temperature butter, one Tbsp at a time. This buttercream sometimes deflates/curdles once all the butter is mixed in, especially if the butter is too warm or cold. But don't worry, it's fixable! Allow the buttercream to continue to mix on a medium-high speed until it comes back together and fluffs up again. This can take anywhere from 3 to 10 minutes. If the frosting still hasn't come back together at this point, please refer to my detailed troubleshooting guide in the post above.
Beat until the butter is fully incorporated and the mixture has reached a fluffy, silky-smooth consistency. Then, mix 1 Tbsp of vanilla extract with 1 tsp of instant coffee (optional) together in a small bowl, and add this mixture, along with 1 tsp of fine salt, into the buttercream while mixing on a low speed.
Next, pour in the melted and cooled chocolate. It should no longer be warm to the touch but still fluid. Mix on a medium speed until the ingredients are combined. Scrape the sides of the bowl as needed with a rubber spatula.