Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper.
Place a large nonstick skillet over medium-high heat. Add the sausage to the skillet and break into small pieces using a wooden spoon. Cook, stirring frequently, until the sausage is browned, about 5 minutes. Drain the fat from the sausage and set aside to cool slightly.
Put the shredded mozzarella in a large mixing bowl. Pour the green food coloring over the cheese and stir thoroughly to combine.
Sprinkle a work surface with all-purpose flour. Stretch the pizza dough out into 2 long rectangles, each 18 inches long and 2 1/2 inches wide. Divide the pesto down the center of the dough rectangles lengthwise, leaving 2 inches of border on each end. Sprinkle the sausage on top of the pesto. Mound the green cheese over the sausage. Working from the long side of the rectangles, tuck both ends in. Wrap the long side of the dough over and around the cheese. Roll the logs like burritos and press the dough together to create a neat seam. Lay the dough logs onto the parchment-lined baking sheet seam-side down. Twist the logs to give the tentacles movement. Squeeze both ends of the logs to make them narrower and tapered.
Whisk the egg whites with 1 tablespoon of water in a small bowl. Pour half of this mixture into a second small bowl. Add 3 drops of the violet food coloring and 5 drops of the super red food coloring to the first bowl to make dark maroon; stir to combine. Add 1 drop violet food coloring and 1 drop super red food coloring to the second bowl to make light maroon; stir to combine.
Using the dark red egg wash, paint both sides of the tentacles, coming only halfway up the log with a pastry brush. Using the light red egg wash, paint the remainder of the tentacles with a second pastry brush. Dot the light red portion of the tentacles with the mini pepperoni slices to create suction cups along the top.
Bake until the pepperoni slices and pizza dough are crisp, 18 to 20 minutes. Allow to cool for 2 minutes before lifting onto a serving platter. To decorate: turn a large stockpot on its side. Arrange the tentacles so they appear to be crawling out of the stockpot. Trim off any green cheese that oozed out while baking and use it to decorate as slime.