Trim the crusts off the bread, squaring up the slices. Cut each slice into fourths.
Toss the shredded cheese into a large bowl, along with the mayonnaise, butter, and heavy cream. Using an electric mixer, beat together on medium speed until blended together.
Add the Worcestershire sauce, the kosher salt, black pepper, dry mustard, and paprika. Stir into the cheese mixture until well combined and smooth.
Lay the bread squares out onto a large surface and spread a small amount of the cheese mixture over half the squares, about 1 teaspoon (by measurement). Don’t use too much on this layer or as the cheese melts in the middle, the squares will slide apart.
Place the remaining squares of bread on top of each.
Set the cheese squares on baking sheets lined with a Silpat liner or with parchment paper.
Divide the remaining cheese mixture over the tops, spreading with a little on the sides of each stack.
Bake the cheese squares in a 375-degree oven for 12 minutes, or until they are a light golden color.