Preheat oven to 375 degrees.  Grease 9×13 casserole dish.  Set aside.

Perform steps in the order listed.

1. Put the first 8 ingredients in a 2 cup liquid measuring cup (rosemary through pepper).  Add the milk.  Microwave on high for 3.5-4 minutes or until very hot.  Stir well.  Cover with plastic wrap.  Set aside to steep.
2. Peel the sweet potatoes and slice into very thin slices (as thin as you can make them).  Slice the onion into thin rounds and then in half (forming half circles).  Peel the parsnips and slice into very thin rounds (as thin as you can make them).
3. Shred the cheese.  Combine the two shredded cheese varieties together.  Set aside 1 cup of the combined shredded cheese to melt on the au gratin the last half of the oven cycle.  The remaining cheese will go into the cheese sauce.
4. In a sauce pan, over medium low heat, melt the butter.  Add the flour and stir constantly for one minute. The mixture should be bubbling. Strain in the milk (leaving the herb sprigs and garlic out) and stir to combine.  Continue stirring until thickened into a pourable sauce consistency (just a few minutes).  Once thickened, take the sauce off of the heat and stir in the shredded cheese (keep the one cup aside for later).  Stir until you have a smooth cheese sauce.  Set aside.
5. In the prepared pan, put a single layer of sliced veggies in this order: potato, parsnip, onion, potato. Pour/Smear the top potato layer with half of the cheese sauce.  Continue layering until you’ve used all of your veggies.  If you run out of one veggie, keep going with the others, finishing with potatoes.  Finish by smearing the top layer of potatoes with the rest of the cheese sauce.  Cover with foil and bake in the oven for 25 minutes.  Take the foil off and sprinkle the reserved 1 cup of cheese over the top.  Put the casserole back in the oven, without foil, for 25 minutes.
6. Once out of the oven, sprinkle with fresh herbs for garnish.  Serve warm.