Add the ham, cream cheese, mayo, parsley, mustard, Worcestershire, pepper, okra brine and shallot to a food processor and pulse until you have a pastelike consistency. (You can make this ahead and store in an airtight container, refrigerated, until ready to serve.)
Spread 1/4 cup deviled ham over a piece of white bread. Top with a slice of pumpernickel bread to form a black-and-white sandwich. Repeat to form 8 sandwiches total. Gently trim the crusts of the sandwiches. Cut each sandwich on the bias to form 2 triangular tea sandwiches. Serve immediately.
Deviled ham is a Southern classic! Some people like to put relish in their deviled ham spread, but I use a special ingredient instead: Pickled okra! The okra gives this spread a pop of acid that is unique and delicious.