Set a large pot of salted water over high heat and bring to a boil.
Add the pasta and cook for 8-10 minutes until just slightly underdone (it will continue cooking in the oven). With a slotted spoon or wire skimmer, remove the pasta from the water and transfer to a large bowl.
In the same water, blanche the broccoli for 5 minutes then remove and place in the same bowl as the pasta. Finally, poach the chicken breasts in the same pot for 7-10 minutes until cooked through.
Remove from the water and allow to rest for a few minutes then cube and add to the pasta and broccoli.
Pour the bechamel sauce over the pasta, chicken and broccoli then add the sour cream and half of the cheese.
Season generously with salt and pepper. Stir to combine then transfer half to an oven-safe baking dish. Sprinkle over the the remaining cheese then top with the rest of the pasta.
Combine the breadcrumbs, parmesan and garlic in a small bowl and drizzle with a little olive oil. Stir together with a fork then sprinkle over the pasta.
Place in the oven and allow to bake for 15-20 minutes until golden brown and bubbling.
Remove from the oven and allow to cool for 5 minutes then serve.