This paper proposes a templated VHDL architecture for P4-programmable packet parsing on FPGAs offering high throughput while occupying a small area footprint. The architecture comprises a multi-stage header parser unit arranged in a pipelined structure. Each header analysis unit is characterized by a set of generic parameters comprising unique features and relations of supported protocols retrieved from the P4 code that describes each stage along the pipeline. Synthesis results of the packet parser show up to 549~Gb/s throughput on a Xilinx Virtex-7 FPGA and 1~Tb/s on a Xilinx UltraScale+ for a twelve-stage pipeline. Compared with state-of-the-art solutions, our proposed architecture performs at higher throughput with acceptable resource utilization.