Combine the 3 cups half and half, garlic, salt, pepper, and Italian seasoning in a large pot and bring to a simmer. Add potatoes and stir to combine. Cover and cook for 10-15 minutes until potatoes are tender.
Stir 3 tablespoons of flour into remaining 1/4 cup half and half. Stir into pot along with 1 cup cheese. Cover and cook another 5 minutes or so until thickened and cheese is completely melted. Stir in bacon.
Transfer potato mixture to a large baking dish. Sprinkle remaining cheese over the top, then sprinkle crushed Saltine crackers over the top of the cheese. Drizzle butter over cracker crumbs. Bake at 400 for 10-15 minutes until cracker topping is browned and sauce is bubbly. (You can broil for the last few minutes if you want your crackers more browned).
Serve hot and top with cracked black pepper and fresh herbs if desired.