Achieving high-performance when developing specialized hardware/software systems requires understanding and improving not only core compute kernels, but also intricate and elusive system-level bottlenecks. Profiling these bottlenecks requires both high-fidelity introspection and the ability to run sufficiently many cycles to execute complex software stacks, a challenging combination. In this work, we enable agile full-system performance optimization for hardware/software systems with FirePerf, a set of novel out-of-band system-level performance profiling capabilities integrated into the open-source FireSim FPGA-accelerated hardware simulation platform. Using out-of-band call stack reconstruction and automatic performance counter insertion, FirePerf enables introspecting into hardware and software at appropriate abstraction levels to rapidly identify opportunities for software optimization and hardware specialization, without disrupting end-to-end system behavior like traditional profiling tools. We demonstrate the capabilities of FirePerf with a case study that optimizes the hardware/software stack of an open-source RISC-V SoC with an Ethernet NIC to achieve 8x end-to-end improvement in achievable bandwidth for networking applications running on Linux. We also deploy a RISC-V Linux kernel optimization discovered with FirePerf on commercial RISC-V silicon, resulting in up to 1.72x improvement in network performance.