Autonomous control of sixth-generation (6G) low Earth orbit satellite networks is hindered by the gap between high-level human intent and low-level control logic: translating a request such as "uninterrupted Arctic video" into a valid reinforcement learning reward still takes days of manual trial and error, and existing large language model translators cannot learn from the failures of the policies they generate. This article presents ALMOND (Agentic Large-Model-Orchestrated autonomous Network Design), a cognitive framework that closes this intent-to-action loop under on-orbit compute constraints. The contribution in artificial intelligence is a bidirectional semantic engine that translates natural-language demands into multi-objective reward functions and, conversely, mines implicit operational constraints from failed reinforcement-learning trajectories through counterfactually validated forensics, together with a large language model-guided graph neuroevolution that seeds and critiques policy architectures. The contribution in engineering is a ground-centric, compute-frugal architecture for autonomous 6G non-terrestrial network operation, in which satellites execute only distilled policies below 50,000 parameters with sub-15 ms inference and no on-board large language model. On a 350-satellite digital twin driven by real ephemeris data, ALMOND raises polar handover success from 55% to over 95%, converges about three times faster than baseline reinforcement learning, and reduces reward engineering from 48 hours to 4.5 hours, demonstrating a practical path toward trustworthy in-orbit autonomy.

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