Preheat oven to 375 degrees and grease an 11×9 pan with butter.
Add the flour and butter to a large bowl and use a pastry blender or fork to blend until the mixture resembles coarse sand. Stir in the sugar, baking powder, salt, and baking soda until combined.
Add the milk and stir until a loose dough begins to form. Transfer the dough to a lightly floured surface and knead until a ball forms.
Make the filling by whisking together the butter, brown sugar, pumpkin pie spice, and ground cinnamon until well combined. Add the pumpkin puree and stir until mixed.
Separate the dough into two equal balls. Roll out the first ball until the dough is around ¼ inch thick.
Spread half the butter mixture over the top of the dough and roll the dough into a log shape. Use a sharp knife to cut the log into six equal pieces. Place each piece in the prepared pan, leaving space between each roll for the cinnamon rolls to spread as they bake.
Repeat the process with the remaining dough.
Place the cinnamon rolls in the preheated oven and bake for 25 to 30 minutes, until they are golden brown on top and cooked through.
While the cinnamon rolls are cooking, make the glaze by beating together the cream cheese, powdered sugar, vanilla, and milk. Add more milk if needed to thin the glaze.
When the cinnamon rolls are done baking, spread the glaze over the top of each cinnamon roll before serving.