© 2017 The Authors. We study the structure, age and metallicity gradients, and dynamical evolution using a cosmological zoom-in simulation of a Milky Way-mass galaxy from the Feedback in Realistic Environments project. In the simulation, stars older than 6 Gyr were formed in a chaotic, bursty mode and have the largest vertical scaleheights (1.5-2.5 kpc) by z = 0, while stars younger than 6 Gyr were formed in a relatively calm, stable disc. The vertical scaleheight increases with stellar age at all radii, because (1) stars that formed earlier were thicker 'at birth', and (2) stars were kinematically heated to an even thicker distribution after formation. Stars of the same age are thicker in the outer disc than in the inner disc (flaring). These lead to positive vertical age gradients and negative radial age gradients. The radial metallicity gradient is negative at the mid-plane, flattens at larger disc height |Z|, and turns positive above |Z| ~ 1.5 kpc. The vertical metallicity gradient is negative at all radii, but is steeper at smaller radii. These trends broadly agree with observations in the Milky Way and can be naturally understood from the age gradients. The vertical stellar density profile can be well described by two components, with scaleheights 200-500 pc and 1-1.5 kpc, respectively. The thick component is a mix of stars older than 4 Gyr, which formed through a combination of several mechanisms. Our results also demonstrate that it is possible to form a thin disc in cosmological simulations even with a strong stellar feedback.