Preheat oven to 200º celsius.
Bring water to boil in a large pot.
Once boiling, cook carrots and broccoli stalks for 3 minutes. Do not remove from water.
To to pot, add pasta and broccoli florets. Cook for a further 8 minutes.
With one minute remaining, add the spinach.
Reserve 1/2 cup of pasta water. Drain remaining pasta/vegetable mixture.
To make the bechamel sauce, melt the butter along with the garlic in a small saucepan at medium heat.
Once the butter begins to bubble, stir through the flour continuously with a wooden spoon for approximately 2 minutes.
Slowly add the mild ( a little at a time), stirring continuously to avoid lumps. Once all the milk has been incorporated , turn down the heat to low and allow to cook for a further 2-3 minutes to thicken.
Remove the saucepan from the heat. Add the parmesan cheese to the bechamel sauce and stir through to combine.
Combine the pasta/vegetables, bechamel sauce and reserved pasta water in the large pot.
Place ingredients into a large baking dish and top with grated cheese.
Bake until golden brown for approximately 30 minutes.