You can buy low loss shielded, twisted-pair cable with RJ11 ends. Effectively the same as an RJ45 cable.
The cable from cabinet to house is probably just bog standard telephone cable, but is not be as subject to mains borne interference as the master socket to router, so better quality cable may help.
Indeed you ~can~ buy that. But what practical use is the shielding? I'm not aware of any domestic market kit that provides an "earth" connection for a shielded RJ11 cable. AFAIK a shielded cable run should have the shield connected to "earth" at one end only in order to avoid problems where the "earths" of the devices at each end are differently terminated (e.g. on different phases or locally grounded rather than using a common supplier provided earth).
Genuine question there, not trying to be a pain! My knowledge is only partial in this area so am happy to be educated