Whisk flour, salt and yeast together in a bowl or mixer.
Whisk milk, honey, 1 egg, melted shortening and melted butter in a 4-cup measuring cup or bowl until honey has dissolved.
Add milk slowly to flour mixture. Mix until a shaggy dough forms and no dry flour remains, about 2 minutes.
Scrape down the sides of the bowl as needed to ensure the dough is fully incorporated.
Knead for 10 minutes until dough is smooth, elastic and comes away from the sides of the bowl.
Transfer dough to lightly floured counter and knead by hand, about 30 seconds, to form smooth, round ball.
Cut a 13-inch long piece of parchment paper and place it in the cooking vessel. Lightly oil or spray the parchment paper.
Place the dough, seam side down, on the parchment paper inside the cooking vessel. Close the lid.
Select Manual/Mode 1– set the temperature to 85°F and set time to 1 hour. Press START.
When proof is complete, remove the dough from the cooking vessel.
Transfer to a clean counter and press down the dough and cut dough into 15 equal pieces. Cover the dough balls with plastic wrap.
Work with 1 piece of dough at a time, keeping the remaining covered. Shape the dough into a ball by stretching dough around your thumbs and pinching edges together so the top is smooth.
Place ball seam side down, and using your cupped hand, roll the dough in small circles until dough is smooth and round. Continue with remaining dough pieces.
Evenly space 10 dough balls, seam side down on the parchment paper that you used before for the first proofing, placing them around the edge of the cooking vessel. Place remaining 5 balls in center, staggering them between seam of balls around edge.
Proof the dough. Select Manual/Mode 1– 85°F and set time 1 hour. Press START.
When proof is complete, preheat the oven to 350°F.
Make egg wash by beating 1 egg with 1 tbsp of water, gently brush the rolls with egg wash before baking.
Place the cooking vessel into the oven and bake uncovered for 40 minutes until the rolls are golden brown.
Remove the cooking vessel and place it on the silicon resting mat. Let rolls cool in the cooking vessel for 15 minutes.
Using the parchment paper, lift the rolls out from the cooking vessel and place on a wire rack to cool.