Large quantum fluctuations might drive magnetic systems to disordered phases even at low temperatures. Recently, a few two-dimensional spin-1/2 systems have been realized in which the isotropic triangular lattice results in the emergence of the quantum spin liquid state.We investigate the spin state of a layered organic material, (EDT-TTF-CONH2)2+[BABCO]- by multi-frequency electron spin resonance measurements. The (EDT-TTF-CONH2)2+ sites form a closely isotropic triangular lattice, and the Brownian motion of the molecular rotor BABCO- layers provoke large dipole fluctuations. We found no indication of magnetic ordering or spin freezing down to 1.5 K. Our results suggest that, due to the intrinsic disorder, a unique QSL state is formed. To verify the absence of the ordering, we intend toperform high-precision muon spin rotation experiments down to 30 mK in low magnetic fields.