Preheat the oven to 350°F (175°C) and line a 12-cup muffin tin with paper liners.
In a medium bowl whisk together the flour, baking powder, baking soda, and salt, then set aside.
In a large bowl beat the softened butter and granulated sugar with a mixer on medium speed until light and fluffy, about 2–3 minutes.
Add the eggs to the butter mixture one at a time, beating well after each addition, then mix in the vanilla extract.
In a small bowl combine the milk and Hennessy and stir to blend.
Add the dry ingredients to the butter mixture in three additions, alternating with the milk-Hennessy mixture, beginning and ending with the dry ingredients, mixing on low just until combined.
Use a spatula to gently scrape down the sides and bottom of the bowl and fold the batter to ensure it is evenly mixed without overmixing.
Divide the batter evenly among the 12 liners, filling each about two-thirds full.
Bake the cupcakes for 16–18 minutes, or until a toothpick inserted in the center comes out clean or with a few moist crumbs.
While the cupcakes bake, make the Hennessy syrup by combining Hennessy, sugar, and water in a small saucepan over low heat, stirring until the sugar dissolves and the mixture slightly thickens, then remove from heat to cool.
Remove the cupcakes from the oven and let them cool in the pan for 5 minutes, then transfer them to a wire rack.
While the cupcakes are still warm, lightly brush the tops with the cooled Hennessy syrup, then allow them to cool completely for about 25 minutes.
For the frosting, beat the softened butter in a large bowl on medium speed until creamy and pale, about 2 minutes.
Gradually add the powdered sugar, 1 cup at a time, beating on low speed until incorporated, then increasing to medium until smooth.
Add the vanilla, salt, and 3 tablespoons of Hennessy, then beat until the frosting is light and fluffy, adding heavy cream or milk 1 teaspoon at a time if needed to reach a smooth piping consistency.
Taste the frosting and, if a stronger Hennessy flavor is desired, beat in up to 1 additional tablespoon of Hennessy, adjusting with a little more powdered sugar if it becomes too soft.
Once the cupcakes are completely cool, transfer the frosting to a piping bag fitted with your desired tip or prepare an offset spatula for spreading.
Pipe or spread the Hennessy buttercream generously onto each cupcake in swirls or mounds.
Optionally garnish the cupcakes with a light dusting of cocoa powder, chocolate shavings, or a tiny drizzle of Hennessy syrup.
Let the frosted cupcakes rest for 10–15 minutes before serving so the flavors meld slightly and the frosting sets.