Preheat the oven to 350°F. Line a 12-cup muffin tin with paper or foil liners.

In a stand mixer, combine melted butter, oil, vanilla, hot coffee, and sugar. Mix until well combined.

In a separate bowl, sift together flour, cocoa powder, baking soda, and salt. Slowly add the dry ingredients to the mixer on low speed.

With the mixer on low, add the egg and buttermilk. Mix until just combined.

Fill muffin tins with batter (about 3/4 full) and bake for 25-30 minutes. Allow cupcakes to cool completely.

In a saucepan, cook sugar over medium heat, stirring every 1-2 minutes until melted and amber in color (about 10-15 minutes).

Remove from heat and immediately stir in butter until combined. Add in heavy cream and salt, whisking until smooth.

Pour the caramel into a heatproof jar or bowl to cool to room temperature.

In a stand mixer, beat room temperature butter, vanilla, salt, and powdered sugar until smooth (1-2 minutes).

Add in heavy cream and caramel sauce, mixing until fully incorporated. Adjust consistency with additional heavy cream if needed.

Pipe the buttercream onto cooled cupcakes using a large star piping tip.

Before serving, drizzle with additional caramel and sprinkle with flaky sea salt.

Store covered at room temperature or in the refrigerator for up to 3 days. Caramel can be stored in the refrigerator for up to 1 month in a sealed container.