Preheat the oven to 350°F (175°C) and line the muffin tin with the paper cupcake liners.

In a mixing bowl whisk together the flour, baking powder, baking soda, and salt, then set aside.

In another bowl beat the softened butter, brown sugar, and granulated sugar with the mixer until light and fluffy, about 3 minutes.

Beat in the eggs one at a time, then mix in the vanilla extract, butter extract, and rum extract until combined.

In a small measuring cup combine the butterscotch soda and milk.

Add the dry ingredients to the butter mixture in two additions, alternating with the soda–milk mixture, beginning and ending with dry ingredients, and mix just until combined.

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.

Transfer the pan to a wire rack and let the cupcakes cool in the pan for 5 minutes, then remove them to cool completely.

While the cupcakes bake, make the butterscotch filling by melting the butter in the small saucepan over medium heat.

Stir in the brown sugar and salt and cook, stirring constantly, until the mixture is bubbly and looks like wet sand, about 2–3 minutes.

Carefully pour in the heavy cream, whisking constantly, and cook for another 2–3 minutes until smooth and slightly thickened.

Remove the saucepan from the heat and stir in the vanilla extract and butter extract, then let the butterscotch cool to room temperature.

For the frosting beat the softened butter and cream cheese together until completely smooth and creamy.

Gradually mix in the powdered sugar on low speed until incorporated, then add 2 tablespoons of the cooled butterscotch sauce, vanilla extract, butter extract, and enough heavy cream to reach a fluffy, pipeable consistency.

Once the cupcakes are completely cool, use a small knife or the end of a piping tip to cut a small core from the center of each cupcake.

Spoon or pipe some of the butterscotch filling into each cupcake center, then replace a bit of the removed cake on top to seal.

Transfer the frosting to a piping bag fitted with a piping tip and pipe swirls of frosting on top of each cupcake.

Drizzle any remaining butterscotch sauce lightly over the frosted cupcakes if desired.

Let the frosted cupcakes rest for 15–20 minutes so the flavors meld before serving.