The star--black hole ( binary known as discovered by the Collaboration is chemically and kinematically associated with the metal-poor ED-2 stream in the Milky Way halo. We explore the possibility that was assembled dynamically in the progenitor globular cluster (GC) of the ED-2 stream. We used a public suite of star-by-star dynamical Monte Carlo models to identify binaries in GCs with different initial masses and (half-mass) radii. We show that a likely progenitor of the ED-2 stream was a relatively low-mass ($ GC with an initial half-mass radius of $ 4\,$pc. Such a GC can dynamically retain a large fraction of its BH population and dissolve on the orbit of ED-2. From the suite of models we find that GCs produce $ binaries, approximately independently of initial GC mass and inversely correlated with initial cluster radius. Scaling the results to the Milky Way GC population, we find that $ of the binaries formed in GCs are ejected from their host GC, all in the early phases of evolution ($ these are expected to no longer be close to streams. The $ of binaries retained until dissolution are expected to form part of streams, such that for an initial mass of the progenitor of ED-2 of a few $10^4\ we expect $ to end up in the stream. GC models with metallicities similar to solar) include binaries with similar BH masses ($ orbital periods, and eccentricities. We predict that the Galactic halo contains of order $10^5$ binaries that formed dynamically in GCs, a fraction of which may readily be detected in Gaia DR4. The detection of these sources provides valuable tests of BH dynamics in clusters and their contribution to gravitational wave sources.