The first nonlinear gyrokinetic turbulence simulations that quantitatively reproduce experimental transport levels in an H-mode pedestal are reported. In the JET-ILW (ITER-like wall) pedestal, the bulk of the transport in the steep gradient region is caused by the turbulence driven by the microtearing mode (MTM). Kinetic ballooning modes are found to be in a second-stability regime. With contributions from the neoclassical and electron temperature gradient driven transport, the MTM mechanism reproduces, quantitatively, the experimental power balance across most of the pedestal.