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.
Leftovers keep well in the fridge and can be reheated gently in the microwave, or wrapped in foil and baked at 350°F in the oven for 10 minutes. They can also be frozen in an airtight container for up to 3 months.