In a small saucepan, whisk together milk and bread flour.
Cook over medium to medium high heat for 1-2 minutes until it thickens and looks like thin mashed potatoes.
Using a rubber spatula, transfer milk roux into the bowl of an electric mixer. Allowed it to cool for 5 minutes.
Add milk, and using a whisk, combine the milk into the milk roux.
In a medium mixing bowl, whisk together the flour, yeast, sugar and salt until well blended.
Add the egg and softened butter into the roux and mix with the dough hook until well blended.
Add the dry ingredients and mix on medium speed until a soft dough forms.
Knead for 5-6 minutes in the mixer or by hand on an unfloured work surface.
Spray a medium bowl with nonstick cooking spray. Place dough in bowl and flip over so the greased side is up.
Leave the dough in a warm place to rise for approximately 1 ½ hours or until dough appears puffed. It will not rise that high.
Spray a 9-inch round cake pan with nonstick cooking spray. Fit a round piece of parchment paper onto the bottom of the pan. Spray parchment with spray.
Place dough onto a work surface. Using a dough cutter divide into 4 equal pieces.
On an unfloured work surface, working with ¼ of the dough at a time, roll into a 12 inch by 6 inch rectangle with the short (6 inch) side closest to you.
Using a ruler and a pizza wheel, lightly mark halfway across the dough. Do not cut through the dough.
Use a small offset spatula, spread 2 tablespoons of pesto on the half of rectangle farthest away from you. Leave a border between 1/8 and ¼ inches uncovered.
Using a pizza wheel, cut the unfilled half of the dough closest to you into very thin strips approximately 1/8 quarter inch wide.
Gently fold the empty border over the filling slightly to prevent the pesto from leaking out.
From the pesto covered side of the dough, gently roll the dough into a tight spiral rolling towards you and over the thin strips forming a log. Roll it so that the seam side is facing down.
Using a very long, sharp knife, gently cut the log in half crosswise. Cut each half in half again forming 4 equal rolls.
Place each roll on the edges of the pan by placing one against the edge and the next rotated 90 degrees close to the first. Repeat with the remaining 2 rolls alternating their placement by 90 degrees.
Repeat steps #13 through #19 three more times.
Continue alternating the rolls by 90 degrees along the edges of the cake pan until there are 10 rolls total around the perimeter of the pan.
Place the next 5 rolls in a smaller circle inside the larger one alternating the positions by 90 degrees again.
Place the last roll in the center. The rolls may not fit tightly together at this point.
Lightly cover the cake pan with plastic wrap and place in a warm place to rise for 60 to 70 minutes. After rising, the rolls should be somewhat touching.
While rolls are rising, preheat the oven to 350°F.
Remove the plastic wrap from over the pan and bake rolls for approximately 28-31 minutes or until the rolls are nice and brown. The rolls will have baked and joined together.
Remove from the oven and gently flip rolls, still joined together, onto a large platter. Flip over again so that they are upright.
Using a pastry brush, lightly brush olive oil over each roll. Lightly sprinkle grated parmesan on top of each rolled. Serve warm.