In the meantime, make the pumpkin butter. Add the pumpkin puree, sugar, pumpkin pie spice, and water into a small saucepan. Set the mixture over medium heat, stirring occasionally until it starts to bubble on top.
Cover the mixture and allow it to simmer for 15 minutes, stirring occasionally to prevent burning on the bottom.
Remove the pumpkin butter from the heat and transfer it into a heat-safe container. Store the pumpkin butter in the fridge until you're ready to assemble the buns.
Once the dough has finished rising, lightly punch it down to remove any excess air in it.
Transfer the dough to a clean, lightly floured surface. Divide the dough into 6 equal pieces, and roll each piece into a ball.
Use a rolling pin to roll each piece out into a ~4" circle. If the dough keeps springing back, let it rest for 5 minutes, then try rolling again.
Transfer the buns to a parchment lined baking sheet, spacing them apart to allow room for spreading. Leave the buns in a warm environment until they puff up a little, ~30 minutes. In the meantime, make the cheesecake filling and streusel.