Renormalisation group (RG) interfaces were introduced by I. Brunner and D. Roggenkamp in 2007. To construct such an interface consider perturbing a UV fixed point, described by a conformal field theory (CFT), by a relevant operator on a half space. Renormalising and letting the resulting QFT flow along the RG flow we obtain a conformal interface between the UV and IR fixed point CFTs. Although enjoying a full conformal symmetry this interface carries information about the RG flow it originated from. In this talk I will consider a rather special case of the RG interface between two boundary conditions of a 2D CFT which is obtained from a boundary RG flow interpolating between two conformal boundary conditions. This interface is zero-dimensional and is thus described by a local boundary-condition changing operator. I investigate its properties in concrete models and formulate a number of general conjectures that can help charting phase diagrams of boundary RG flows.