Preheat the oven to 400 degrees . Carve a 2-inch-deep rectangular slice out of the top of the bread, leaving 1 inch on the sides and the bottom. Cut the bread top crosswise into 1-inch slices. Transfer the bread bowl to a parchment-lined baking sheet. Place 1/2 cup giardiniera and 1/2 cup salami in the bottom; top with three-quarters of the prosciutto.
In a medium saucepan, melt the butter over medium-high. Add the flour; whisk until smooth. Pour in 1 cup half-and-half and bring to a simmer, whisking constantly. Reduce the heat to medium-low and simmer, whisking occasionally, until thickened, about 6 minutes. Add the cheese; stir until melted, adding more half-and-half if the sauce is too thick to pour. Season with salt and pepper.
Pour the cheese sauce into the bread bowl. Top with the remaining giardiniera, salami and prosciutto; top with the tomato. Bake 10 minutes. Put the bread-top slices on the baking sheet. Bake until the cheese sauce is hot and the bread is toasted, about 10 minutes. Garnish with the lettuce; serve with the bread.