High-energy neutrinos detected by the IceCube Observatory provide an exclusive opportunity to study the origin of cosmic rays and the nature of the sources producing them. Blazars are among the proposed birthplaces for the astrophysical high-energy neutrinos. Our studies (Buson et al., 2022 and 2023) put forward a small set of blazars as likely counterparts to IceCube neutrinos. In this contribution, we focus on this well-defined sample of objects in order to characterize the nature of the sources and the peculiarities of their central engine. Thanks to archival and proprietary data, we provide new insights into the intrinsic properties of this sub-population of neutrino-emitter blazars. We carry out a comprehensive investigation of the observational and physical properties that govern the physics of these blazars, among which redshifts, black hole masses, accretion regimes, radiation fields, etc. Such properties can provide us with crucial clues to decipher what may make this set of objects capable of accelerating cosmic rays. We will discuss our findings, and place our results in the general context of the properties displayed by the overall blazar population.