Beurre Manie. Mix equal parts soft butter and all purpose flour and mix it in while the gravy is boiling and whisk until thickened.

Went cornstarch last night and it was sublime.

After roasting the carrot/garlic/celery/onion combination in the morning, I added them to a 5:2 beef broth and red wine mixture and has it simmer for three hours with a teaspoon of Veggie Better Than Bullion. When time to serve I added another 1/4 of wine and broth mix and the cornstarch when boiling.

Assuming it's to go with meat then ensure you've some onion, celery etc under the meat (like a trivet) when roasting. Take the meat out, remove excess but not all fat, put the pan on the hob, add flour and cook it out. No need for a roux as the meat fat serves the same purpose as the butter. Add alcohol of choice and simmer briefly to remove the alcohol (optional but recommended). Add stock, herbs of choice, jams (if for poultry or pork, again optional) and cook down. Mash, sieve and serve.

Not much flour is needed as you've the veg also thickening it, if dealing with gluten issues then rice flour works almost as well.

We've had friends fighting over who can take the leftover gravy home with them on the rare occasions there were left overs.

I dont like the texture cornstarch gives, similarly with xanthan gum and various other agents. Can't say I recall trying to use arrowroot but it typically doesn't stand to reheating so wouldn't be our first choice.

Haha, I think it all depends on personal preference.
I understand what you said about cornstarch being more convenient. Indeed, it dissolves quickly and is less fussy to work with. It's easy to achieve the desired thickness for the gravy. there isn't much difference in taste.