Prepare a grill fire to 325° with pecan or hickory for smoke flavor.
Slice garlic into thin slices with a mandoline slicer or sharp knife.
Add butter to a small skillet with the garlic slices.
Place over low heat. As the butter melts, add in ground rosemary, thyme and pepper.
Continue to cook, keeping a constant watch on the garlic, and stirring often until garlic is toasted and lightly browned. Do not burn the garlic.
Remove from heat and set aside 5 minutes.
Stir in brown sugar until dissolved.
Place whole salmon fillet on a sheet pan, skin side down.
Using a sharp knife, slice down the center of the salmon in the thickest part, but not all the way through. This creates a channel for the garlic butter.
Pour garlic butter with toasted garlic chips over the salmon and spread evenly.
Place salmon, skin side down on the grill over indirect fire with the grill lid closed.
Grill for about 15 minutes, check with a digital thermometer in the thickest part of the salmon. Cook until salmon reaches 145°. The total cook time will be about 20- 25 minutes total depending on the thickness of your salmon.
Remove from grill to a serving platter. Garnish with lemon slices and fresh herbs if desired.
Serve immediately.