We discuss laser micromachining as a means of fabricating dielectric-based electrospray thrusters that use ionic liquid propellants for nanosatellite propulsion applications. Because of their small size, nanosats typically lack means of propulsion, which limits their lifetimes and mission scopes and is problematic for deorbit at end of life. Electrospray thrusters, however, can be very compact, using electric potentials to accelerate and eject ionic matter, thereby achieving high specific impulse. Traditional fabrication methods involve numerous steps, including lithography and/or chemical etching, resulting in microscale emitter structures that protrude from a substrate and can easily be damaged during assembly and/or launch. This format also requires a separate, detached grid electrode that serves as an extraction grid needed to induce ionic emission of propellant from the emitters. Our fabrication approach uses Bessel-beam laser micromachining to form embedded, micron-diameter capillaries up to several hundred microns long through a transparent glass substrate, without chemical etching. One surface of the glass is coated with a transparent conductive layer that serves as an integrated extraction electrode and which needs no alignment. Further laser machining with Gaussian-beam, water-assisted cavitation is used to excavate cylindrical electrospray cavities in this surface around each capillary, to catch errant propellant and prevent shorting while optimizing the capillary emitter-extractor separation distance. The resulting array of capillary emitters and cavities with integrated extractor comprises an electrospray emitter chip that forms the core of an electrospray thruster, and provides the potential to achieve significantly lower onset voltages than traditional electrospray thruster designs.