Put the bacon in a large nonstick skillet over medium heat and cook, stirring, until golden brown and crispy, about 10 minutes. Transfer to a paper towel-lined plate to drain. Reserve the bacon fat.
Add the bacon fat to a griddle over medium heat. Place the bread on the griddle and lightly toast one side. Remove from the griddle and arrange toasted-side down on a work surface. Divide 2 cups of the cheese and all of the bacon, tomatoes and chives over 4 slices of bread. Top with the other 4 slices of bread, toasted-side up, to make 4 sandwiches.
Divide 1/2 cup of the remaining cheese into 4 piles on the griddle and place a sandwich over each pile, pressing down. Griddle for a few minutes until the cheese is browning and melted. Divide the remaining 1/2 cup of cheese into 4 piles on the griddle?one next to each sandwich. Then flip each sandwich onto a pile of cheese and cook for a couple of minutes until the center of each is melted.