This work examines the effect of the absolute pressure (0.1 or 1.0 MPa) and the addition of a high-ash rejected material from municipal solid waste (MSW) composting (RC) on the slow pyrolysis of two-phase olive mill waste (OW). The experiments were conducted in a batch pyrolysis system using an initial mass of 750 g of feedstock. Three types of initial materials were tested: the OW alone, a mixture of OW and pure additives (5 wt % K2CO3 and 5 wt % CaO), and a mixture of OW and RC (10 wt %). For the OW without any additive, an increased pressure led to a market increase in the carbonization efficiency (i.e., fixed carbon yield). At atmospheric pressure, the addition of either additives (CaO + K2CO3) or RC led to important changes in the pyrolysis behavior as a result of the catalytic role of the alkali and alkaline earth metals (AAEMs). However, this catalytic effect, which is translated into an enhancement of the decomposition of both the hemicellulose and cellulose fractions, was not observed at 1.0 MPa. The potential stability of all of the produced biochars appeared to be very high, given the results obtained from both proximate and ultimate analyses. This high stability was confirmed by C-13 and H-1 solid-state nuclear magnetic resonance, which showed that the carbon contained in the biochars was composed mainly or entirely of highly condensed aromatic structures. However, the highest values of stable C (Edinburgh stability tool) and R-50,R-x (recalcitrance index) were obtained for biochars produced from the OW + RC mixtures at any pressure. In summary, the addition of the rejected material from MSW composting appears to be a very cost-effective measure to obtain a potentially high-stable biochar, even at atmospheric pressure.