List category shortcode w/ custom formatting

Is there any plugin with a shortcode that could do this?

Show posts from a category, USING A CUSTOM OUTPUT.

I’ve looked at
WP Category Post List
and
Category Shortcode
which are part of the way there, they will list posts from a category, but they don’t seem to let me set my own template for how to output them. I would like something that lets me customize how it outputs the list.

Like I’ve got it outputting categories how I like it in category.php, if I could just copy and paste that into a custom.php for the corresponding shortcode, that would be perfect.