When conventional phase shifter based arrays are used in millimeter-wave systems, the angle of departure (AoD) and angle of arrival (AoA) estimates are obtained through high-overhead exhaustive beam sweeping (EBS). Recently, true-time-delay arrays re-emerged as a promising architecture for fast angle estimation. In this work, we develop an algorithm for joint AoD and AoA estimation using only one Orthogonal Frequency Division Multiplexing (OFDM) symbol and frequency-dependent beams that can be synthesized by fully digital and true-time-delay arrays. We compare the developed algorithm with wideband single-carrier based EBS in terms of the misalignment probability and required training overhead. Numerical simulations in millimeter-wave channels reveal the advantages of the proposed algorithm.