Heat the olive oil in a saucepan over medium-low heat. Once warm, add in the garlic and red pepper flakes. Cook, stirring occasionally, until the garlic is just golden. Turn off the heat and set it aside.
Season the chicken all over with salt and pepper. Brush a bit of the garlic oil on the chicken too. Heat a grill pan over medium-high heat. Add the chicken and grill about 5 to 6 minutes per side. Continue to grill until cooked through and the internal temperature reads 165 degrees F.
Set the chicken aside to rest for 10 minutes. Preheat the oven to 425 degrees F. Line a baking sheet with parchment paper.
After 10 minutes, slice or chop the chicken.
Toss the broccoli florets with 1 to 2 teaspoons of the garlic oil. Add a pinch of salt and pepper and toss.
Place the sheet of puff pastry on the parchment paper. Poke it all over with a fork - this helps keep it from bubbling up.
Take a few spoonfuls of the garlic sauce and spread it all over the puff pastry, leaving a 1-inch border for crust. Top with 1 cup of shredded cheese.
Add on the chopped chicken and the broccoli florets. Sprinkle on the remaining ½ cup cheese. Brush the outside edges with the egg wash.
Bake for 18 to 22 minutes, or until golden and puffy and flaky. Top with parmesan cheese.
Let cool slightly before slicing.