Neighbor discovery (ND) protocols are used for establishing a first contact between multiple wireless devices. The energy consumption and discovery latency of this procedure are determined by the parametrization of the protocol. In most existing protocols, reception and transmission are temporally coupled. Such schemes are referred to as \textit{slotted}, for which the problem of finding optimized parametrizations has been studied thoroughly in the literature. However, slotted approaches are not efficient in applications in which new devices join the network gradually and only the joining devices and a master node need to run the ND protocol simultaneously. For example, this is typically the case in IoT scenarios or Bluetooth Low Energy (BLE) piconets. Here, protocols in which packets are transmitted with periodic intervals (PI) can achieve significantly lower worst-case latencies than slotted ones. For this class of protocols, optimal parameter values remain unknown. To address this, we propose an optimization framework for PI-based BLE-like protocols, which translates any specified duty-cycle (and therefore energy budget) into a set of optimized parameter values. We show that the parametrizations resulting from one variant of our proposed scheme are optimal when one receiver discovers one transmitter, and no other parametrization or ND protocol - neither slotted nor slotless - can guarantee lower discovery latencies for a given duty-cycle in this scenario. Since the resulting protocol utilizes the channel more aggressively than other ND protocols, beacons will collide more frequently. Hence, due to collisions, the rate of successful discoveries gracefully decreases for larger numbers of devices discovering each other simultaneously. We also propose a scheme for configuring the BLE protocol (and not just BLE-\textit{like} protocols).