The mixed layer is the uppermost layer of the ocean, connecting the atmosphere to the subsurface ocean through atmospheric fluxes. It is subject to pronounced seasonal variations: it deepens in winter due to buoyancy loss and shallows in spring while heat flux increases and restratifies the water column. A mixed-layer depth (MLD) modulation over this seasonal cycle has been observed within mesoscale eddies. Taking advantage of the numerous Argo floats deployed and trapped within large Mediterranean anticyclones over the last decades, we reveal for the first time this modulation at a 10 d temporal scale, free of the smoothing effect of composite approaches. The analysis of 16 continuous MLD time series inside 13 long-lived anticyclones at a fine temporal scale brings to light the importance of the eddy pre-existing vertical structure in setting the MLD modulation by mesoscale eddies. Extreme MLD anomalies of up to 330 m are observed when the winter mixed layer connects with a pre-existing subsurface anticyclonic core, greatly accelerating mixed-layer deepening. The winter MLD sometimes does not achieve such connection but homogenizes another subsurface layer, then forming a multi-core anticyclone with spring restratification. An MLD restratification delay is always observed, reaching more than 2 months in 3 out the 16 MLD time series. The water column starts to restratify outside anticyclones, while the mixed layer keeps deepening and cooling at the eddy core for a longer time. These new elements provide new keys for understanding anticyclone vertical-structure formation and evolution.