We present CARMA, the Cluster Ages to Reconstruct the Milky Way Assembly project, the aim of which is to determine precise and accurate age measurements for the entire system of known Galactic globular clusters (GCs) and to use them to trace the most significant merger events experienced by the Milky Way. The strength of CARMA relies on the use of homogeneous photometry, theoretical isochrones, and statistical methods, which will enable us to define a systematic uncertainty-free chronological scale for the complete sample of Milky Way GCs. In this paper, we describe the CARMA framework in detail, and present a first application on a sample of six metal-rich GCs, with the aim being to unequivocally elucidate the debated origin of NGC 6388 and NGC 6441. Our results demonstrate that this pair of clusters is coeval with another four systems that have a clear in situ origin. Moreover, their location in the age-metallicity plane matches that occupied by in situ field stars. The accurate age comparison enabled by the CARMA methodology rules out the possibility that NGC 6388 and NGC 6441 were accreted as part of a past merger event.