Hyde here from Shopify. Great question!
The Brooklyn theme allows you, natively, to create a home page slideshow that's either full width or adapted to the height of the first image in the sequence.
The size and shape of the slideshow will depend on the size and shape of the customer's device as all Shopify's free themes are responsive. So sometimes your slideshow images will be cropped on some screens and full image on others.
In fact, there is a full list of all available settings for your slideshow in this help document here:
Anything over or beyond this will require some custom coding. If you are on a paid plan with Shopify you have an hour of free design time to avail of, so you can let me know here if you'd like the theme team to reduce that slideshow height.
All the best, Hyde.