I'd like to roast carrots, parsnips, broccoli and cauliflower in olive oil. Will all these roast ok together or do I need to add the broccoli and cauliflower at a later point?
It depends on how well done you like them. I would start them all together, and start checking them after 15 or 20 minutes or after you have turned them; remove any vegetables that are done to your taste and continue roasting the rest. Either keep them warm in a 250 oven but roasted vegetables are usually fine at slightly warmer than room temp. Usually carrots and parsnips do take extra time.
I agree with "Tarragon". Also, cut the root veggies smaller so they cook faster - leaving the softer vegetables larger. Another option is to partially cook the root vegetables first, then do your roasting. You may want to experiment with each group individually to have a more accurate idea.
This is a bit off-topic, but Ming Tsai shows how to cut carrots to carmelize better/faster----slice on diagonal X1, rotate carrot 180 degrees and slice again on diagonal, rotate, etc. This increases the surface area. Very cool!
Rather than try to remove the broccoli from the mix I'd add it in only about 15 minutes before end time. It cooks the quickest