Combine warm milk, yeast, honey, and butter in a bowl; stir. Add salt and most of the flour, reserving the rest for dusting. Stir using a wooden spoon until a sticky dough forms.
Dust a work surface with the leftover flour. Knead the dough until smooth, elastic, and no longer sticky, adding more flour as needed. Form dough into a ball that springs back lightly when pressed.
Transfer dough to a lightly greased bowl, cover with greased foil, and let rise in a warm place until doubled in size, about 1 1/2 hours.
Meanwhile, cut kitchen string into 4 dozen 8- to 10-inch strands. Place strings in a bowl and toss with oil to coat; set aside.
Press risen dough down on a work surface; reserve 3 to 4 tablespoons for forming “stems.” Cut remaining dough in half and cut each half into 6 wedges. Roll each into a round ball by cupping your hand over the dough and pressing and rolling lightly in a circular motion for 10 to 15 seconds. Cover and let rest for 15 minutes.
Preheat the oven to 375 degrees F (190 degrees C). Line 2 baking sheets with silicone liners.
Place 4 pieces of string on your work surface. Crisscross strings over a center point into a star formation. Place a dough ball, smooth side-down, onto the center point. Firmly tie each string into a knot over the center of the roll. Snip off excess string using scissors.
Place tied roll onto a prepared baking sheet, knot side-down. Repeat with remaining strings and dough balls.
Let rolls rise for about 30 minutes.
Sift a little flour on top of rolls. Shape reserved dough into “stems” and place them on the sheet next to the rolls.
Bake in the center of the preheated oven until lightly browned, 20 to 25 minutes.
Remove from the oven and let cool until safe to handle, about 15 minutes. Cut strings off of each roll at the tops and peel down carefully and slowly to remove. Cut a small hole in the tops of each roll and press “stems” into each hole. Transfer pumpkin rolls to a serving platter.