@xavi In my case, I added some meta tags in my HTML's <head> for Open Graph and one specific for Birdsite (to show previews with large images).
You can check the OG (OpenGraph) tags here: https://ogp.me/
For the other one, you can probably find it searching for "Birdsite Summary Card with Large Image".
If you use a CMS or a static-site generator, maybe you can search for a plugin to do it even easier.
And BTW, Mastodon still doesn't have big image previews :( https://github.com/mastodon/mastodon/issues/19984