  Spectral winding of complex eigenenergies represents a topological aspect
unique in non-Hermitian systems, which vanishes in one-dimensional (1D) systems
under the open boundary conditions (OBC). In this work, we discover a boundary
spectral winding in two-dimensional non-Hermitian systems under the OBC,
originating from the interplay between Hermitian boundary localization and
non-Hermitian non-reciprocal pumping. Such a nontrivial boundary topology is
demonstrated in a non-Hermitian breathing Kagome model with a triangle
geometry, whose 1D boundary mimics a 1D non-Hermitian system under the periodic
boundary conditions with nontrivial spectral winding. In a trapezoidal
geometry, such a boundary spectral winding can even co-exist with corner
accumulation of edge states, instead of extended ones along 1D boundary of a
triangle geometry. An OBC type of hybrid skin-topological effect may also
emerge in a trapezoidal geometry, provided the boundary spectral winding
completely vanishes. By studying the Green's function, we unveil that the
boundary spectral winding can be detected from a topological response of the
system to a local driving field, offering a realistic method to extract the
nontrivial boundary topology for experimental studies.
