Preheat oven to 350°. Line mini muffin pans with paper liners.
Whisk together flour, cocoa, sugar, baking soda, baking powder, and salt. Add eggs, buttermilk, oil, vanilla, and water. Using an electric mixer on low speed, mix until smooth.
Fill muffin pans about 2/3 full. Bake about 15 minutes, or until a toothpick inserted in the center comes out clean. Cool in pans on wire racks about 10 minutes. Remove cupcakes to wire racks to let cool completely.
Cupcakes can be stored overnight at room temperature or frozen in an airtight container for up to a month.
Salted Caramel Filling
Heat sugar, water, and corn syrup in a heavy saucepan over high heat. Stir occasionally until syrup is clear. Attach a candy thermometer to side of pan. Stop stirring, and cook until syrup comes to a boil, washing down sides of pan with a wet pastry brush as needed.
Boil, gently swirling pan occasionally, until mixture is caramelized and temperature just reaches 360°.
Remove from heat. Slowly pour in cream and stir with a wooden spoon until smooth. Stir in sea salt. Use immediately. If caramel begins to harden, reheat gently until pourable.
Use a paring knife, cut a cone-shaped piece, about 1/2-inch deep, from the center of each cupcake. Spoon 1-2 teaspoons of warm filling into each cupcake. Sprinkle a pinch of sea salt over filling.
Dark Chocolate Frosting
Combine cocoa and boiling water. Stir until cocoa has dissolved.
Using an electric mixer on medium-high speed, beat butter, confectioners’ sugar, and salt until pale and fluffy. Reduce speed to low and add melted and cooled chocolate. Beat until combined. Beat in cocoa mixture.
Frosting can be refrigerated up to 5 days or frozen up to 1 month. Bring to room temperature and beat on low speed until smooth before using.
Fit a pastry bag with a medium open-star tip (Wilton #18). Fill pastry bag with frosting. Pipe onto cupcakes, swirling tip and releasing as you pull up to form a peak. Garnish with a pinch of sea salt.
Cupcakes are best eaten the day they are filled and frosted. Store at room temperature in an air-tight container until ready to serve.
Makes about 56 mini cupcakes.