Punching strengthening of reinforced-concrete slabs using a bonded reinforced-concrete overlay (BRCO) is an efficient alternative to traditional strengthening systems such as post-installed shear reinforcement, enlargement of the support column, or bonded fibre-reinforced polymer strips. The BRCO technique allows for both the flexural stiffness and shear strength of existing slabs to be increased. Shear strength increases due to the greater slab thickness, while an increase in flexural stiffness is also provided by the added reinforcement. Particular attention must be paid to the interface between the existing slab and the BRCO, because performance gains can only be achieved if the existing slab and the new concrete layer work monolithically. Interface performance can be improved through surface preparation and mechanical connectors; the latter is recommended to avoid premature debonding failure. This paper presents an ad hoc design approach for flat slabs strengthened with BRCO based on the critical shear crack theory, which accounts for slab rotation after strengthening. This is a fundamental parameter to assess the punching capacity of the strengthened slab. The efficiency of the proposed method is confirmed by the agreement between analytical results and experimental data collected during an experimental campaign carried out at the Universidade Nova de Lisboa.