Boron carbonyl complexes have received considerable attention in recent years due to their unique structures and bonding. With inspiration from the newly observed first boron carbonyl aromatics (BCAs) B13(CO)n+ (n = 1-7) and based on joint chemisorption experiments and first-principles theory investigations, we report herein observation of the first boron carbonyl complexes B11(CO)n+ (n = 1-6) and B15(CO)n+ (n = 1-5) with π and σ conflicting aromaticity analogous to benzene C6H6 and cyclooctatetraene C8H8 in π-bonding, respectively, with B15(CO)n+ being the largest boron carbonyl complexes observed to date, enriching the structures and bonding of boron carbonyls effectively. B11+ and B15+ which can chemisorb up to six and five CO molecules under ambient conditions, respectively, are found to be much more reactive towards the first CO than the magic-number aromatic B13+. Extensive theoretical analyses unveil both the chemisorption pathways and potential energy profiles of these interesting species. Detailed bonding pattern analyses show that quasi-planar B11(CO)n+ (6π + 8σ) exhibit global 6π aromaticity and 8σ antiaromaticity, while B15(CO)n+ (8π + 10σ + 4σ) possess global 8π antiaromaticity and 10σ aromaticity, as well as local 4σ antiaromaticity for the B4 core, inheriting the delocalized bonding patterns of their parent B11+ (B2@B9+) and B15+ (B4@B11+) monocations, respectively. Both naked B11+ and B15+ appear to have much higher chemisorption reaction rates toward CO than B13+, while their carbonyl complexes B11(CO)n+ and B15(CO)n+ with conflicting aromaticity are found to possess obviously larger average coordination energies per CO than the previously observed BCAs B13(CO)n+