To make the olive tapenade, first combine the olives, anchovy paste, garlic, and capers in a food processor fitted with a steel blade and pulse 3 to 4 times only.
Add the olive oil, mustard, lemon juice, thyme, and parsley and process until chunky.
Arrange the pieces of bread on a cookie sheet and brush one side of each piece with olive oil.
Approximately 15 minutes before serving, toast the bread until golden brown in the oven, about 8 minutes total making sure to flip them once halfway through.
On each of the slices of toast, spread the burrata (or place a slice of the fresh mozzarella) and top with your desired amount of tapenade. (Note: Reserve a portion of the tapenade to serve in a dish alongside the red pepper slices if choosing to follow the optional recipe variation.)