In a small saucepan, warm the milk to about 110 F. Pour it into a large mixing bowl. Stir in 1/4 cup honey until it dissolves. Sprinkle the yeast over the milk-honey mixture. Let it sit for about 5-7 minutes, or until the mixture becomes foamy.
Once the yeast is activated, whisk in the egg and pumpkin puree until well combined. Gradually fold in the all-purpose flour and salt by hand or by using a stand mixer fitted with the dough hook attachment. Continue mixing until the dough begins to come together. Add in 2 tablespoons of softened butter to the dough and mix on low for about 10 minutes, or until the dough becomes smooth and elastic.
Lightly grease a large bowl. Transfer the dough to the bowl and turn it around to coat it with a thin layer of grease. Cover the bowl with plastic wrap or a damp towel and let it sit in a warm, draft-free spot for 1-2 hours, or until it has doubled in size.
Lightly grease a baking pan. Once the dough has risen, punch it down gently and turn it out onto a lightly floured surface. Divide the dough into 12-16 equal pieces. Shape each piece into a ball and arrange them in the prepared baking pan.
Cover the pan loosely with plastic wrap or a damp towel and let the rolls rise for another hour or until they've puffed up nicely.
Preheat your oven to 375 F. In a small dish, melt the remaining 2 tablespoons of butter. Stir in the 2 teaspoons of honey to create a glaze.
Gently brush the honey-butter glaze all over the tops of the risen rolls.
Place the baking pan in the preheated oven and bake for 20-22 minutes, or until the rolls are golden brown and sound hollow when tapped.
Remove the rolls from the oven and allow them to cool slightly on a wire rack.