What is the name of the dish consisting of a filling covered with batter?

Pick your favorite fruit with cinnamon and some type of sugar, cover with a basic batter and enjoy.

never heard of a cobbler with batter rather than scone type dough on the too

Isn't a cobbler, someone who repairs or makes shoes? We have a fish called a Cobbler in Western Australia.

I like blueberry and peach cobbler.

Kiwozzie, batter is like a wet dough, the word is used for many things including cake

We (in Australia and New Zealand) call batter the crispy coating on deep fried fish, this question is describing fruit covered with a cake or sponge cake mixture then cooked.