Optical frequency combs (OFCs) are frequency rulers essential for precision metrology, next generation navigation, and testing of fundamental physics. Despite intense efforts, chip-integrated OFCs remain laboratory-bound, unable to fulfill their promise of compact and cost-effective deployment. While improvements in fabrication and integration are important, a conceptual limitation has stymied progress: on-chip OFC architectures have aimed to miniaturize their table-top counterparts and relied on cascading outward from a single pump. In integrated platforms, this approach does not readily generate the strong, low-noise, octave-spaced signals crucial for robust zero-frequency offset detection. Here, we overcome this limitation via an architectural inversion where an optical microcomb fills the spectrum between two octave-separated pumps. The two pumps generate a parametrically driven cavity soliton (PDCS) in an integrated χ⁽³⁾ resonator, which robustly self-aligns to both pumps across multiple foundry-fabricated devices and operating configurations. This produces a single octave-spanning comb from telecom to visible wavelengths, whose zero-frequency offset is defined by the pumps' harmonic offset and can therefore be reliably detected and stabilized. We showcase our platform's capabilities by executing all of the three core tasks of OFC metrology: optical frequency synthesis, low-noise millimeter-wave generation, and integrated optical clock readout, using the same self-aligned microcomb with only its input locks changed.