Place butter and minced garlic in a small bowl. Melt butter and mix.
Cut sourdough bread lengthwise and width making about 1 inch squares. Make these cuts deep so you can fill with cheese. Use caution not to cut completely through.
Generously brush garlic butter mixture into the cut areas.
Stuff the cut areas with mozzarella cheese as far down as you can. Don't fill completely. Leave a small amount of room at the top of the cut.
Fill remainder of cut area with shredded cheddar cheese.
Brush garlic butter over the entire top of the sourdough loaf.
Wrap in foil to seal. Place on grill or campfire rotating every 10-15 minutes. When cheese is melted remove from fire and open foil.
Sprinkle additional cheese over the top of the bread and place over fire until melted. Remove from foil and serve warm.