Preheat oven to 180 degrees celcius. Season Chicken with salt and pepper and place on an oven tray lined with baking paper. Drizzle with 1 tablespoon olive oil and roast for 50-55 minutes or until cooked through.
Remove from oven and stand for 15 minutes. Once cooled, discard skin, pull meat off bone and tear into bite size pieces.
Place cream, garlic and thyme in a small saucepan over medium heat. Bring to a simmer then turn off heat to let flavours infuse.
Blanch brocooli in a medium pot of salted boiling water for about 4 minutes, until just tender. Drain and set aside on paper towels to absorb any extra water.
Place broccoli in a food processeor and pour in the cream mixture (discarding the thyme). Blend until smooth. Season to taste with salt and pepper.
Add chicken and cook for 3-4 mintues until reheated. Pour broccoli sauce over chicken and toss to combine.
Drain pasta and add to frying pan. Carefully combine and pour onto serving platter. Garnish with parmesan and serve immediately.