I'm cooking two different dishes in the oven at the same time that each require different temperatures. One is a roasted vegetable dish that says to cook at 475 for 35-40 minutes and the other is parmesan crusted pork chops at 350 for 40-45 minutes. What do you suggest I do?
I would put the oven on 350, and cook the pork chops according to the recipe. Put in the vegetables for the last 30 minutes. Once the pork chops are done, cover them and let them rest for 15-20 minutes. In the mean time, turn up the temperature to 475 and finish cooking the vegetables for 15-20 minutes.
The reason I suggest you adapt the temperature to the pork chops is that they are most likely to dry out if you deviate from the recipe. Roasted veggies on the other hand are almost fail safe. The first 30 minutes on a low temp will start cooking them, and the last few minutes will add some crispiness to them.
Roast veg at 475 for 30 min first. This can happen earlier and if more than 2 hours in advance refrigerated. Turn oven down. Roast chops. Remove chops. While they are resting return oven to 475 and finish veg for 5 - 10 minutes.
...or...set oven for 350. Roast chops. After 20 minutes add veg to oven. Remove chops when they are done and turn oven up to 475 to finish veg.
See, an understanding of roasting is important here. Your veg will cook at 350...the higher heat will allow them to caramelize. Timing is important though, you don't want dry veg or pork.