In a small bowl, combine the granulated sugar, brown sugar, cinnamon, and pumpkin pie spice.
Grease 12 muffin tins with butter.
Divide the risen dough in half. Place one half on a lightly floured surface and keep the other covered in the bowl.
Roll the dough into a thin, even sheet.
Spread half of the softened butter over the top of the dough, all the way to the edges.
Evenly cover with half of the cinnamon sugar filling, pressing down into the butter to make it stick. Cut the sheet into six even strips.
Stack the strips with the cinnamon side on top. Cut the stacked strips into 6 equal pieces.
Gently transfer the stacked pieces to the prepared muffin tins, cut side up, lightly separating the layers at the top.
Repeat with remaining dough and filling. Cover the tins loosely with a towel or plastic. Allow to rise until puffed, 30 minutes.
Preheat oven to 375˚F (190˚C).
Bake the fantails in the preheated oven until golden brown, 18-22 minutes. Allow to cool in the pan for 10 minutes, then gently transfer to the wire rack.