We propose a high-quality deterministic single-photon source which can not only works in the ultrastrong light-matter coupling regime, but also emits two single photons with an arbitrary time separation, in one excitation process. We find that the special solutions of the two-qubit quantum Rabi and Jaynes-Cummings models which have at most one photon and constant eigenenergies can be used to implement this proposal through two consecutive adiabatic evolutions, and the system goes back to the initial state of the next period automatically after photon emission. Due to their peculiarities and reach of the ultrastrong coupling, the adiabatic evolution can be quite fast and further accelerated with the Stark shift. This Letter paves the way to fast quantum information protocols which take advantage of the ultrastrong coupling and avoid its dynamical complexity simultaneously.