Stir together the pepper jelly and mustard in a small bowl.
To assemble the sandwiches, lay 4 slices of the bread on a cutting board. Top each with 3 slices Boar's Head Ichiban Teriyaki™ Style Chicken, one-quarter of the avocado and 2 slices Boar's Head Bold 3 Pepper Colby™ Jack Cheese. Spread the pepper jelly mixture on one side of the remaining 4 slices of bread, sprinkle with salt and pepper and then top each of the sandwiches with a slice.
Melt 1 tablespoon of the butter on a grill pan over medium-low heat. Spread the outsides of the sandwiches with the remaining 2 tablespoons butter. Add the sandwiches to the grill pan and toast until the cheese begins to melt and the bottoms are crisp and golden, 3 to 4 minutes. Press down with a metal spatula to compress the sandwiches, then flip them. Toast the other side, pressing again, until crisp and golden, another 3 to 4 minutes. Cut in half and serve.
If you don't have a grill pan, you can cook 2 sandwiches at a time in a large skillet. Keep the sandwiches warm on a baking sheet in the oven at 200 degrees F while you make the remaining sandwiches. Add an additional tablespoon of butter to the skillet for the second batch.