In a large skillet, cook bacon slices completely. Take out of pan, pat remaining grease off and set aside.
Set up sandwiches by spreading blackberry jam on four pieces of bread. Top with cheese and bacon slices and put on remaining slices of bread to complete four sandwiches.
Spread softened butter or margarine on top of each sandwich bread and grill in large skillet over medium-high heat on butter side down. While that is cooking, spread butter over slices of bread that is facing up now. Flip over when bread is brown to cook other slice of bread.
Take out of skillet and put on a plate. Let sandwich sit for about 1-2 minutes before cutting in half. This helps to set up cheese so it doesn't spill out of sandwich.