Cook pasta according to the box instructions, drain and set aside in a bowl.
Cook chicken in a skillet over medium heat with some salt and olive oil, until completely cooked. Set aside until cooled enough to be handled.
In the same skillet, add spinach and chopped broccoli. Add some salt, lemon juice and minced garlic. Saute over medium heat until spinach is cooked down and broccoli is tender. Add veggies to the bowl with pasta.
Chop chicken and add it to the bowl with pasta as well.
Preheat the oven to 350 and lightly grease a casserole dish.
Stir pasta, chicken and veggies together with some salt and fresh parsley, then transfer to the casserole dish.
In the same skillet as you cooked veggies and chicken, heat up some oil.
Dice shallots and saute in the skillet until fragrant.
Add heavy cream and slowly whisk in sour cream until incorporated. Add dry and fresh grated Parmesan cheeses and some salt. Bring to simmer on medium heat and simmer, stirring slowly, for a couple of minutes. Pour sauce over pasta mixture, evenly.
Grate a generous amount of fresh Parmesan cheese over the top and bake for 15-17 minutes.