We report the discovery of 15 exceptionally luminous 10 ≲ z ≲ 14 candidate galaxies discovered in the first 0.28 deg2 of JWST/NIRCam imaging from the COSMOS-Web survey. These sources span rest-frame UV magnitudes of −20.5 > MUV > −22, and thus constitute the most intrinsically luminous z ≳ 10 candidates identified by JWST to date. Selected via NIRCam imaging, deep ground-based observations corroborate their detection and help significantly constrain their photometric redshifts. We analyze their spectral energy distributions using multiple open-source codes and evaluate the probability of low-redshift solutions; we conclude that 12/15 (80%) are likely genuine z ≳ 10 sources and 3/15 (20%) likely low-redshift contaminants. Three of our z ∼ 12 candidates push the limits of early stellar mass assembly: they have estimated stellar masses ∼ 5 × 109M⊙, implying an effective stellar baryon fraction of ε⋆ ∼ 0.2−0.5, where ε⋆ ≡ M⋆/(fbMhalo). The assembly of such stellar reservoirs is made possible due to rapid, burst-driven star formation on timescales < 100 Myr where the star formation rate may far outpace the growth of the underlying dark matter halos. This is supported by the similar volume densities inferred for M⋆ ∼ 1010M⊙ galaxies relative to M⋆ ∼ 109M⊙—both about 10−6 Mpc−3—implying they live in halos of comparable mass. At such high redshifts, the duty cycle for starbursts would be of order unity, which could cause the observed change in the shape of the UV luminosity function from a double power law to a Schechter function at z ≈ 8. Spectroscopic redshift confirmation and ensuing constraints of their masses will be critical to understand how, and if, such early massive galaxies push the limits of galaxy formation in the Lambda cold dark matter paradigm.