Cook the pasta and broccoli: divide the broccoli into small florets. Bring a large pot of well-salted water to a boil. Cook the pasta 2 minutes less than it says on the package and the broccoli for 2 minutes. So, my pasta takes 10 minutes to cook so I cooked it for 8 minutes and after 6 minutes of cooking time, I've added the broccoli (to the same pot) and cook them together for 2 more minutes. Drain the pasta and broccoli and add to a 9x13 inch (23×33 cm) oval casserole dish.
Preheat the oven to 375°F/190°C/Gas Mark 5 (if you have a convection oven reduce the temperature by about 20° or follow the manufacturer's instructions).
Prepare the chicken: cut the chicken into 1-inch (2-3 cm) cubes. Mix the olive oil with the spices, add to the chicken. Season with salt and pepper and toss to coat. Add the chicken to the casserole dish (chicken doesn't have to be cooked).
Make the pesto cream sauce: whisk the flour with milk until combined then whisk in the cream and pesto. Season the sauce lightly with salt and pepper. Add the sauce to the casserole dish.
Assemble: Stir everything together. Top with shredded cheese.
Bake for 35 minutes or until the chicken is cooked through, the cheese golden and the sauce bubbly.
Enjoy!