Your options depend on your oven. If your oven cooks fast thus cooking the outside of a calzone but the inside is not cooked, you need to heat the inside first by…
grilling what goes inside your calzones
No griddle? Get shallow round pans and put ingredients on pan and heat up in oven.
I actually grill all my calzones inside- it makes for a great calzone.
Give it a try.
ALso, you have to decide on how you will coat your calzone. Before, during or after will also have an effect on cooking. I don’t brush anything on my calzones until they are out of the oven then I lightly hit with butter and parm
I have oiled and sprnkled salt and pepper on before cooking but I and my customers love the light butter and parm.