Pour the lukewarm milk into the bowl of a stand mixer and then add the sugar. Stir until the sugar and salt until dissolved. Sprinkle the yeast on top and allow to sit for 3-5 minutes or until foamy.
Add 2 tablespoons of the butter, the pumpkin puree, shredded cheese and half of the chopped rosemary. Add in 1 cup of the flour and mix with the dough hook.
Add in flour one cup at a time until the dough pulls away from the side of the bowl and is tacky but not sticky to the touch.
Roll out the dough onto a lightly floured surface and knead for 2-3 minutes or until the dough is soft and elastic. Coat a bowl with olive oil and place the dough in it, turning once to coat the dough. Cover with plastic wrap or a kitchen towel and set aside in a warm place to rise for 1 hour.
Line a baking sheet with parchment paper. Punch down the dough and divide into 12 evenly sized pieces. Cover the dough with plastic wrap or a kitchen towel and let rise for 30 minutes.
Preheat the oven to 350 degrees.
In a small bowl, add the melted butter and rosemary.
Brush the mixture over the rolls and sprinkle with the shredded cheese and kosher salt.
Bake for 18-22 minutes or until golden brown.
Transfer to a wire rack to cool slightly before serving.