Place slivers of butter in a bread canister.
Warm half-and-half in microwave for about 1 ½ to 2 minutes at 50% power.
Pour half-and-half into bread canister.
Add bread flour and sugar, then top with salt and dry yeast.
Turn on “dough” setting.
This will take about 1 hour 45 minutes.
Remove dough from breadmaker and form into 12 balls.
Stretch the tops of the dough on top and fold underneath to smooth out the wrinkles.
Grease a 9x13” glass baking dish generously with butter.
Place rolls in baking dish.
In a measuring cup melt butter.
Add garlic powder, oregano, parsley and basil.
Brush butter mixture generously over top of the dinner rolls.
Heat oven for one minute.
Place rolls in oven.
Every 15-20 minutes, heat the oven again for one minute.
Do this about 5 or 6 times until the rolls raise to the top of the baking dish.
This will take approximately one hour and 30 minutes (sometimes as long as two hours).
Leave rolls in oven and turn on oven to 350°.
Set timer for 25 minutes.
The rolls should be done by then, but check to see that the middle of the pan is no longer doughy.
If they are, cook another 5 minutes or so.
Remove rolls from oven.
Brush with remaining butter mixture.
Then sprinkle the rolls very carefully with the grated parmesan cheese being careful to give full coverage to the rolls.
Serve.