<p>Quantum oscillations in magnetization or resistivity are a defining feature of metals in a magnetic field. The phenomenon is generally not expected in insulators without a Fermi surface. Its observation in Kondo and other correlated insulators provided counterexamples and remains poorly understood. Here we report the observation of resistivity oscillations in a gate-controlled excitonic insulator realized in Coulomb-coupled electron–hole double layers. When the electron or hole cyclotron energy is tuned to exceed the exciton binding energy, recurring transitions arise between the excitonic insulator and layer-decoupled quantum Hall states. Compressibility measurements show an oscillatory exciton binding energy as a function of the magnetic field and electron–hole pair density. Coulomb drag measurements further reveal the signature of finite-angular-momentum excitonic correlations. These findings are qualitatively captured by mean-field calculations. Our study establishes a highly tunable platform based on electron–hole double layers for studying quantum oscillations in correlated insulators.</p>