Parcooking carrots and green beans for an already well-seasoned casserole I will be heating an otherwise perfectly-seasoned casserole dish for an hour.  (Time constraint non-negotiable! But temperature flexible.)  I want to add fresh carrots and green beans but am wondering how long to parcook them (respectively) so they will be just right after an hour in a very moist dish of meat and veloute.  Any suggestions?
In my experience, carrots at about 1.5-2cm thickness will be cooked through after an hour at a bare simmer. You might consider slightly browning, rather than boiling them before adding them to the mixture, for flavor, and to get them up to temperature. As for green beans, (depending on how you like them ) add them 10 -15 minutes before the end of your cooking time?

But if you really don't want to shift the flavor, why not cook them exactly to your liking and add them right at the end, just before service? More like a garnish than an ingredient. Plenty of traditional French stews do this with bacon, caramelized onions, mushrooms .. etc.