Preheat oven to 350° F.
Cook pasta in salted water for about 2 minutes less than package directions in a large pot.
Drain the pasta reserving about half a cup of that starchy pasta water.
Meanwhile, in a blender or food processor on high speed, blend the spinach with the milk until smooth.
In the same large pasta pot, melt the butter and then add the flour, whisking continuously over low-medium heat for 2-3 minutes to create a roux. Slowly whisk in the milk mixture and bring to a boil.
Reduce heat and simmer, whisking occasionally, 3 to 4 minutes, or until sauce is gently bubbling and starting to thicken.
Add reserved pasta water and cheese and whisk until melted.
Microwave the broccoli until slightly tender to give it a bit of a head start.
Stir in the pasta, broccoli and peas gently mixing until combined.
Transfer to a greased baking dish and top with a spinkle of parmesan (we used individual portion baking dishes) and bake for 20 minutes. Pasta should be set.