So when I try to place a call on my iPhone, I click on the phone icon to place a call.

I am constantly greeted with a menu that asks me if I want to:

Edit Home Screen
View most recent voicemail
Create new contact
Search for contact
View most recent call

How can one disable this feature? I think they are called 'quick action menus' and were added with pOS 13.2.

I can't figure out how to get rid of these. Throwing the phone across the room does not seem to help. Thanks.

I just tried it on mine. You are pushing down to hard. It thinks your trying to bring up the other menus. Just tap it with your finger don't push.
You might want to reset your tap and double tap in settings.
Give it a try and let us know.

I think it may be also how long the OP is touching the phone icon. Like Mr Sig suggested, light quick tap.