Mineral-polymer composites found in nature exhibit exceptional structural properties essential to their function, and transferring these attributes to the synthetic design of functional materials holds promise across various sectors. Biomimetic fabrication of nanocomposites introduces new pathways for advanced material design and explores biomineralization strategies. This study presents a novel approach for producing single platelet nanocomposites composed of CaCO₃ and biomimetic peptoid (N-substituted glycines) polymers, akin to the bricks found in the brick-and-mortar structure of nacre, the inner layer of certain mollusc shells. The significant aspect of the proposed strategy is the use of organic peptoid nanosheets as the scaffolds for brick formation, along with their controlled mineralization in solution. Here, we employ the B28 peptoid nanosheet as a scaffold, which readily forms free-floating zwitterionic bilayers in aqueous solution. The peptoid nanosheets were mineralized under consistent initial conditions (σ_calcite = 1.2, pH 9.00), with variations in mixing conditions and supersaturation profiles over time aimed at controlling the final product. Nanosheets were mineralized in both feedback control experiments, where supersaturation was continuously replenished by titrant addition and in batch experiments without a feedback loop. Complete coverage of the nanosheet surface by amorphous calcium carbonate was achieved under specific conditions with feedback control mineralization, whereas vaterite was the primary CaCO₃ phase observed after batch experiments. Thermodynamic calculations suggest that time-dependent supersaturation profiles as well as the spatial distribution of supersaturation are effective controls for tuning the mineralization extent and product. We anticipate that the control strategies outlined in this work can serve as a foundation for the advanced and scalable fabrication of nanocomposites as building blocks for nacre-mimetic and functional materials.