To add onto this, those are raster tiles and the industry is moving away from raster tiles for a multitude of reasons. Headway doesn't bulk-download tiles from OSM, by default it takes an OSM extract from BBBike (with explicit permission) and brings up a server based on that. It generates vector tiles with planetiler and serves them with tileserver-gl-light. I've put a lot of thought into the way it all works in an effort to minimize load on the OSM ecosystem's infrastructure, provide attribution where required, etc.

I can promise you that there's no one-line replacement for the work I've done here unless you want to go out and pay for a closed-source product.

Their data is also subject to this policy: https://wiki.openstreetmap.org/wiki/OpenStreetMap_License

They also heavily discourage bulk downloading tiles so I'm not sure if you're that much better off building your own tile server.