In a large bowl, or the bowl of a stand mixer fitted with the dough hook, mix together the water, flour, yeast, olive oil, honey, and salt.
Pulse the mixture (or stir with a wooden spoon if mixing by hand) until it comes together into a ball.
Knead for 5 minutes by machine, 10 by hand until the dough is smooth.
If the dough is still looking dry and really shaggy after a couple minutes of kneading, add more water, a tablespoon at a time. If it is really sticky and not coming together into a smooth ball, add more flour, a tablespoon at a time.
Cover the bowl and let the dough rest for 10 minutes.
Preheat the oven to 350 °F.
On a lightly oiled surface, roll out the dough into a 1/2-inch thick rectangle.
Spread the pesto sauce over top, leaving a 1/2-inch space on the edges.
Spread the cooked chicken over top of the sauce and cover it with the shredded cheese.
Roll up the dough starting on a long edge into a tight cylinder and pinch the seam to seal it.
Place the roll seam side down and slice it into 12 rolls.
Place each roll, cut side down, onto a parchment lined (or greased) baking sheet and cover the rolls loosely with plastic wrap.
Let them rise for 15-20 minutes to puff up a bit.
Bake for 25-30 minutes or until the pizza rolls are lightly browned and the cheese is bubbling.
Let cool for 5 minutes on the baking sheet and serve warm, drizzled with balsamic glaze if desired.