Preheat the oven to 350 degrees. Line a muffin tin with cupcake liners.

In a large bowl cream together the butter, brown sugar, and granulated sugar.

Stir in the eggs. Add the vanilla bean paste and the butternut squash and mix well.

In a medium bowl mix together the flour, baking powder, baking soda, salt, and spices.

Add the dry ingredients to the wet ingredients and mix until combined.

Fill the muffin cups all 3/4 of the way full with the cupcake batter.

Bake for 20-22 minutes. Remove from the oven and cool completely on a wire rack.

To make the frosting put the butter in a large bowl and beat with a mixer until smooth.

Add the powdered sugar a half cup at a time, beating for 1 minute after each addition, until you have added 3 cups.

Add the milk and caramel sauce and mix well.

Add the remaining powdered sugar until the frosting is the desired consistency.

Mix in the vanilla bean paste and sea salt by hand.

Pipe the frosting onto the cooled cupcakes. Drizzle with additional frosting if desired.