Combine milk and 3 tablespoons butter in a microwave-safe bowl; heat in microwave until butter is just melted and milk is warmed (120 degrees F/49 degrees C to 130 degrees F/54 degrees C), 30 to 60 seconds.
Mix pumpkin, white sugar, and salt together in a bowl; beat in egg and yeast. Stir milk mixture into pumpkin mixture until evenly combined.
Whisk all-purpose flour and bread flour together in a bowl and divide mixture in half. Beat 1/2 the flour mixture into the pumpkin mixture on low until well mixed, about 5 minutes. Add remaining flour mixture and beat until dough is very soft.
Turn dough into a bowl that has been greased or sprayed with cooking spray; lightly grease or spray dough. Cover bowl with a damp cloth and let rise in a warm area until dough is doubled in size, about 1 hour.
Grease or spray an oblong baking sheet with cooking spray.
Punch the risen dough down and turn onto a well floured work surface; knead until dough is smooth and easy to handle, 1 to 2 minutes. Roll dough into a 10x12-inch rectangle and brush top with melted butter. Sprinkle cinnamon, brown sugar, pecans, and currants, respectively, onto the butter layer. Roll dough, beginning with long side, around filling in a jelly roll fashion and pinch the other side onto the roll to seal. Cut roll into 12 slices.
Arrange rolls, cut-side up, on the prepared baking sheet. Cover with a towel and let rise until nearly doubled in size, 30 to 45 minutes.
Preheat oven to 350 degrees F (175 degrees C).
Remove towel from rolls and bake rolls in the preheated oven until golden, about 20 minutes.
Beat cream cheese and 1/2 cup butter together in a bowl using an electric mixer until smooth; beat in confectioners' sugar and vanilla extract until icing is fluffy and smooth. Spread icing on pumpkin rolls.
For best rising in cold climate, heat your oven to lowest setting (about 150 degrees F/65 degrees C). Turn off oven and after five minutes of cooling with door shut, put your covered dough in oven to rise.
I like to use dental floss to cut the roll into the 12 slices, lifting dough and putting the floss under, then crossing over top, pulling to cut. Rolls don't get squashed and there is no knife for dough to stick to.
Per Serving: 521 calories;23.3 g fat;
75.1 g carbohydrates;
5.5 g protein;
72 mg cholesterol;
192 mg sodium.