If you use the "Share" icon on the right of openstreetmap.org, one of the options is to export to an image. You can set a custom box, select output format, and (I think this is what you want) select a custom scaling factor so that the image is "zoomed in" to the level you want. Be aware that the more detail, the bigger the image you're going to get. Once you get the image, you should be able to print that image file the way you want.want. If you need something more complicated, you may want to try a tool like [Maperitive](https://wiki.openstreetmap.org/wiki/Maperitive).

If you use the "Share" icon on the right of openstreetmap.org, one of the options is to export to an image. You can set a custom box, select output format, and (I think this is what you want) select a custom scaling factor so that the image is "zoomed in" to the level you want. Be aware that the more detail, the bigger the image you're going to get. Once you get the image, you should be able to print that image file the way you want.