In the bowl (stand mixer) combine the milk, honey, eggs, butter, 3 ½ cups flour, yeast and salt. Using the dough hook, mix until the flour is completely incorporated. If the dough seems sticky, add the remaining ½ cup of flour.
Cover the bowl with plastic wrap and let sit at room temperature for 1 hour or until doubled in size.
Preheat the oven to 350 degrees F. Line a 9x13 inch baking dish with parchment.
Lightly dust your work surface with flour. Roll out the dough into a rectangle about 10 x 16 inches. Spread the pesto evenly over the dough. Sprinkle the broccoli pieces and cheddar mix evenly over the pesto, lightly pushing it into the pesto. Starting with the long edge closest to you, carefully roll the dough into a log, keeping it fairly tight as you go. When you reach the edge, pinch along the edge to seal. Using a string cut into rolls. Place the rolls in the prepared baking dish. Cover with plastic wrap and let rise 20-30 minutes.
Sprinkle with more cheddar cheese. Bake the rolls for 20-25 minutes, or until the cheese is bubbling. Serve warm and enjoy.