To prepare the cupcakes, warm baking chocolate and buttermilk in a small saucepan over low heat, mixing occasionally, until the chocolate has melted and the mixture is evenly combined. Turn off heat and set aside.
Whisk together flour, cocoa powder, baking power, baking soda, and salt in a small bowl. Set aside.
In the bowl of a standing electric mixer, beat butter and sugar together on medium speed until light and fluffy, about 5 minutes. Add eggs, one at a time, mixing well after each addition. Continue beating until creamy and smooth, about 2 minutes more. Add vanilla extract and mix to combine.
Add half the flour mixture and stir briefly before stirring in the buttermilk-chocolate mixture. Add remaining flour mixture and chocolate chips, stirring until just combined. Divide batter evenly among 12 greased or paper-lined muffin cups.
Bake cupcakes at 350° F for about 20 minutes, until well risen and a skewer or toothpick inserted into the center of one emerges with nearly done-looking chunky crumbs clinging to it; if the consistency looks gooey, continue baking for another minute or two.
Set pan on a cooling rack and cool cupcakes completely in the pan. Just before frosting, insert a thin spatula down the side of each cup to help you lift cupcakes from the pan.
To prepare the frosting, combine sugar and water in a small saucepan. Bring to a boil over medium-high heat, cooking without stirring until the mixture turns dark amber in color.
Remove sugar mixture from heat and slowly add the cream, stirring carefully with a wooden spoon until combined (the mixture will steam and bubble up quite a bit). Add vanilla and salt and stir until completely smooth. Set the caramel sauce aside, uncovered, until cool to the touch, at least 30 minutes.
In the bowl of a standing electric mixer fitted with the paddle attachment, beat butter on medium-high speed until light and fluffy, about 3 minutes. Reduce speed to low and add powdered sugar, mixing until completely incorporated. Turn off the mixer and scrape in the caramel sauce. Beat frosting on low speed to combine before increasing the mixer speed to medium-high. Beat until airy and evenly mixed, about 2 minutes. If the frosting seems too soft to use right away, refrigerate for 10 to 20 minutes to stiffen it up a bit.
Pipe frosting atop the cooled cupcakes or frost them generously with a small spatula. Refrigerate to set the frosting, if desired.