Direct numerical simulations (DNS) of nucleate boiling in the microlayer regime must resolve micron-thin liquid films beneath millimetric bubbles while accounting for conjugate heat transfer in the heater. Although experimental diagnostics have greatly improved microlayer characterisation, they remain limited near the contact line and during rapid transients, motivating complementary high-fidelity simulations. Recent DNS studies have progressively incorporated microlayer physics and conjugate heat transfer, but their high computational cost has generally restricted simulations to sub-millisecond or few-millisecond durations, far shorter than a complete nucleation-detachment cycle. We present a numerical framework which is able to fully resolve the evolution of the microlayer in an accurate yet efficient manner by leveraging quadtree adaptive mesh refinement (AMR). Building on the geometric volume-of-fluid (VOF) phase-change formulation of Cipriano et al. within the Basilisk framework, we introduce a ghost-fluid treatment that enforces the interfacial velocity jump without the spurious oscillations associated with the approximate projection method. Conjugate heat transfer is solved implicitly in a fully coupled manner with the liquid and gas temperature fields, while interfacial non-equilibrium is modelled via an equivalent conductive resistance at the solid-fluid boundary. Verification on a benchmark Stefan problem demonstrates convergence, while validation against the MIT single-bubble experiments of Bucci and al. reproduces heater superheat and bubble growth trends while reducing the computational cost by three orders of magnitude. Sensitivity studies show that contact-angle effects on growth diminish for θ < 15%, and that changes in evaporation are primarily mediated by microlayer area variations: as θ increases from 5% to 30%, the microlayer contribution to total evaporated mass drops from 31% to 25%, whereas the total average mass flux remains nearly constant. Finally, we directly simulate a complete bubble cycle up to 18 ms, enabling discussion of long-time effects such as contact angle hysteresis and interfacial heat transfer resistance.