The detection of complex organic molecules (COMs) toward cold sources such as pre-stellar cores (with T < 10 K) has challenged our understanding of the formation processes of COMs in the interstellar medium. Recent modeling on COM chemistry at low temperatures has provided new insight into these processes predicting that COM formation depends strongly on parameters such as visual extinction and the level of CO freeze out. We report deep observations of COMs toward two positions in the L1544 pre-stellar core: the dense, highly extinguished continuum peak with A ≥ 30 mag within the inner 2700 au; and a low-density shell with average A ∼ 7.5-8 mag located at 4000 au from the core's center and bright in CHOH. Our observations show that CHO, C...