The conventional way of generating optical waveforms relies on in-phase and quadrature (IQ) modulation of a continuous-wave (CW) laser tone. In this case, the bandwidth of the resulting optical waveform is limited by the underlying electronic components, in particular by the digital-to-analog converters (DACs) generating the drive signals for the IQ modulator. This bandwidth bottleneck can be overcome by using a concept known as optical arbitrary waveform generation (OAWG), where multiple IQ modulators and DACs are operated in parallel to first synthesize individual spectral slices, which are subsequently combined to form a single ultra-broadband arbitrary optical waveform. However, targeted synthesis of arbitrary optical waveforms from multiple spectral slices has so far been hampered by difficulties to maintain the correct optical phase relationship between the slices. In this paper, we propose and demonstrate spectrally sliced OAWG with active phase stabilization, which permits targeted synthesis of truly arbitrary optical waveforms. We demonstrate the viability of the scheme by synthesizing optical waveforms with record-high bandwidths of up to 325 GHz from four individually generated optical tributaries. In a proof-of-concept experiment, we use the OAWG system to generate 32QAM data signals at symbol rates of up to 320 GBd, which we transmit over 87 km of single-mode fiber and receive by a two-channel non-sliced optical arbitrary waveform measurement (OAWM) system, achieving excellent signal quality. We believe that our scheme can unlock the full potential of OAWG and disrupt a wide range of applications in high-speed optical communications, photonic-electronic digital-to-analog conversion, as well as advanced test and measurement in science and industry.