Podcast listening is often grounded in a set of favorite shows, while listener intent can evolve over time. This combination of stable preferences and changing intent motivates recommendation approaches that support both familiarity and exploration. Traditional recommender systems typically emphasize long-term interaction patterns, and are less explicitly designed to incorporate rich contextual signals or flexible, intent-aware discovery objectives. In this setting, models that can jointly reason over semantics, context, and user state offer a promising direction. Large Language Models (LLMs) provide strong semantic reasoning and contextual conditioning for discovery-oriented recommendation, but deploying them in production introduces challenges in catalog grounding, user-level personalization, and latency-critical serving. We address these challenges with GLIDE, a production-scale generative recommender for podcast discovery at Spotify. GLIDE formulates recommendation as an instruction-following task over a discretized catalog using Semantic IDs, enabling grounded generation over a large inventory. The model conditions on recent listening history and lightweight user context, while injecting long-term user embeddings as soft prompts to capture stable preferences under strict inference constraints. We evaluate GLIDE using offline retrieval metrics, human judgments, and LLM-based evaluation, and validate its impact through large-scale online A/B testing. Across experiments involving millions of users, GLIDE increases non-habitual podcast streaming on Spotify home surface by up to 5.4% and new-show discovery by up to 14.3%, while meeting production cost and latency constraints.