The statistics of galactic-scale quasar pairs can elucidate our understanding of the dynamical evolution of supermassive black hole (SMBH) pairs, the duty cycles of quasar activity in mergers, or even the nature of dark matter, but they have been challenging to measure at cosmic noon, the prime epoch of massive galaxy and SMBH formation. Here we measure a double quasar fraction of ∼6.2 ± 0.5 × 10−4 integrated over ∼0.″3–3″ separations (projected physical separations of ∼3–30 kpc at z ∼ 2) in luminous (L
bol > 1045.8 erg s−1) unobscured quasars at 1.5 < z < 3.5 using Gaia EDR3-resolved pairs around SDSS DR16 quasars. The measurement was based on a sample of 60 Gaia-resolved double quasars (out of 487 Gaia pairs dominated by quasar+star superpositions) at these separations, corrected for pair completeness in Gaia, which we quantify as functions of pair separation, magnitude of the primary, and magnitude contrast. The double quasar fraction increases toward smaller separations by a factor of ∼5 over these scales. The division between physical quasar pairs and lensed quasars in our sample is currently unknown, requiring dedicated follow-up observations (in particular, deep, subarcsecond-resolution IR imaging for the closest pairs). Intriguingly, at this point, the observed pair statistics are in rough agreement with theoretical predictions both for the lensed quasar population in mock catalogs and for dual quasars in cosmological hydrodynamic simulations. Upcoming wide-field imaging/spectroscopic space missions such as Euclid, CSST, and Roman, combined with targeted follow-up observations, will conclusively measure the abundances and host galaxy properties of galactic-scale quasar pairs, offset AGNs, and subarcsecond lensed quasars across cosmic time.