Coat the chicken breasts on both sides with the blackened spice mix.
Heat the butter over medium heat in a cast-iron skillet. Cook the chicken halfway, about 5 minutes. Flip and repeat until the center is no longer pink, 5 to 6 more minutes. Let the chicken rest before slicing against the grain into 1/4-inch-thick pieces.
Toast the bread, then spread 1 to 1 1/2 tablespoons almond butter on one side of each of 4 slices. Spread 1 tablespoon pepper jam on one side of each of the remaining 4 slices. Divide the chicken among the 4 slices with almond butter, then top each sandwich with a pepper jam slice.