In a small bowl combine the thyme, oregano, garlic, rosemary, salt and pepper. Mix well with a fork or whisk.
Add ground beef to a bowl.
Mix in the seasonings, mushrooms, onions and garlic until well combined.
Form into 1/3 pound meatballs and place on a lined baking sheet.
Prepare a grill fire to 350° on a charcoal grill using hickory or pecan chunks for smoke flavor.
Cook the meatballs over indirect fire with the grill closed 10 minutes.
Turn the meatballs and continue to cook until internal temperature reaches 165°.
Remove from grill to a platter or sheet pan. Cover loosely with foil.
Make the parmesan cream sauce by melting butter in a pan. Whisk in flour.
Cook over medium heat, whisking often, about 4- 5 minutes.
Whisk in the heavy cream and milk until sauce thickens.
Remove from heat. Add salt and pepper.
Whisk in the grated parmesan cheese until smooth.
Make the sandwiches: Butter the buns and toast under the broiler or on the grill.
Slice meatballs in half.
Spread parmesan sauce onto the bottoms of the buns. Top with meatball halves. Drizzle with additional parmesan sauce and add the top buns.
Serve immediately.