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Time crystals represent temporal analogues of the spatial self-ordering exhibited by atomic or molecular building blocks of solid-state crystals. The pursuit of discrete time crystals (DTCs) in periodically forced Floquet closed systems has revealed how they can evade thermalization and loss of temporal order. Recently, it has been shown that even with coupling to the ambient and its concomitant noise, some states maintain their time crystalline order, forming dissipative DTCs. Here, we introduce a scheme for the realization and state control of dissipative DTCs hinging on pumping a Kerr optical resonator with a phase-modulated continuous-wave laser. We show the possible symmetry breaking states possess temporal long-range order and analyze the phase noise of the accompanying signature radio frequency (RF) subharmonic. Besides offering a technique for generating high-spectral-purity RF signals, this versatile platform empowers controlled switching between various DTC states through accessible experimental knobs, hence facilitating the future study of DTC phase transitions. Discrete time crystals are a new state of matter emerging via spontaneous discrete translational symmetry breaking in time. The authors demonstrate that a dissipative discrete time crystal appears in an optical microcavity pumped by a phase-modulated continuous wave laser, offering a new route to study this exotic crystal phase. [ABSTRACT FROM AUTHOR]