In this paper we present a new approach to efficient true-time-delay (TTD) beamforming for large adaptive phased arrays as well as its elegant and compact optical implementation. This Broadband and Efficient Adaptive Method for Time-delay Array Processing (BEAMTAP) algorithm decreases the number of tapped delay lines required to process an N-element phased array antenna from N to only 2, producing an enormous savings in delay-line hardware, especially for large arrays, while still providing the full N M degrees of freedom of a conventional N element time delay beamformer with AI taps each. This allows the system to fully and optimally adapt to an arbitrarily complex spatio-temporal signal environment that can contain broadband signals, noise, and narrowband and broadband jammers, all of which can arrive from arbitrary ranges and angles onto an arbitrarily shaped array. thus enabling a variety of application in radar, sonar, and communication. This algorithm is an excellent match with the capabilities of RF photonic systems using gratings in photorefractive crystals as adaptive weights, because the hardware implementation of tapped delay lines is the factor which limits the scalability of these systems to large arrays. Because the number of available adaptive coefficients in a photorefractive crystal is practically unlimited, these photonic systems can adaptively control very large l-D or 2-D phased arrays, that are well beyond the capabilities of conventional RF or real-time digital signal processing techniques.