In a medium saucepan, over medium heat, melt the butter.
Add the fresh garlic and saute until the garlic is lightly browned.
Add a dash of salt and fresh ground pepper and stir.
Sprinkle the flour over the butter/garlic mixture and stir around. You want to use enough flour to soak up the butter, but not so much that you end up with a super heavy dough. The goal here is to create roux.
Cook this mixture for about 4 minutes, stirring consistently to keep it from burning. This will help remove that "raw" taste that the flour will have. You want the flour to be very lightly browned.
After you've cooked the flour, pour the cream and milk in and use a whisk vigorously until all the clumps of flour are gone and the mixture starts to thicken.
Slowly start adding the shredded Parmesan, while continuing to whisk. Don't stop whisking or else you'll end up with clumpy sauce. This is the slowest part of the making this sauce. Add the cheese little by little until it's all incorporated.
Remove from heat and taste for salt and pepper. Adjust as needed.
This sauce can be refrigerated and reheated. I have never frozen it and reheated it, but I think it would probably do fine. To reheat, slowly heat over low heat while whisking. You may need to add a little milk or cream in order to get it to the right consistency. Careful not to heat it too fast.