Several possible background sources determine the detectability of pep and CNO solar neutrinos in organic liquid scintillator detectors. Among such sources, the cosmogenic 11C nuclide plays a central role. 11C is produced underground in reactions induced by the residual cosmic muon flux. Experimental data available for the effective cross section for 11C by muons indicate that 11C will be the dominant source of background for the observation of pep and CNO neutrinos. 11C decays are expected to total a rate 2.5 (20) times higher than the combined rate of pep and CNO neutrinos in Borexino (KamLAND) in the energy window preferred for the pep measurement, between 0.8 and 1.3 MeV. This study examines the production mechanism of 11C by muon-induced showers in organic liquid scintillators with a novel approach: for the first time, we perform a detailed ab initio calculation of the production of a cosmogenic nuclide, 11C, taking into consideration all relevant production channels. Results of the calculation are compared with the effective cross sections measured by target experiments in muon beams. This paper also discusses a technique for reduction of background from 11C in organic liquid scintillator detectors, which allows to identify on a one-by-one basis and remove from the data set a large fraction of 11C decays. The background reduction technique hinges on an idea proposed by Martin Deutsch, who suggested that a neutron must be ejected in every interaction producing a 11C nuclide from 12C. 11C events are tagged by a three-fold coincidence with the parent muon track and the subsequent neutron capture on protons.