Process Optimization and Quality Characterization of Indocalamus latifolius Leaf–White Tea

White tea (WT) and Indocalamus latifolius leaves (ILLs) are valued for their distinctive aromas and bioactive properties. In this study, flavonoid extraction from ILLs was optimized using total flavonoid yield as the response variable through single-factor experiments and response surface methodology. The resulting Indocalamus latifolius leaf extract (ILLE) was vacuum-concentrated and sprayed onto WT to produce Indocalamus latifolius leaf–white tea (IT). The effects of spray ratio, spraying liquid temperature, and drying temperature on the sensory and chemical qualities of IT were further evaluated. Untargeted metabolomics was performed to compare the metabolite profiles of IT and WT. The optimal extraction conditions for ILLs’ flavonoids were 95 °C, 120 min, and a liquid-to-solid ratio of 60:1 mL/g, yielding 4.39 mg/g total flavonoids. The optimal processing parameters for IT were a spray ratio of 1:1.75 g/g, a spraying liquid temperature of 50 °C, and a drying temperature of 105 °C. Compared with WT, IT showed improved sensory and biochemical qualities, including a richer and more persistent ILLs aroma, a more refreshing and more layered taste, and significantly higher levels of water extracts, flavonoids, tea polyphenols, soluble sugars, and amino acids (p < 0.05). Metabolomic analysis revealed clear compositional differentiation between IT and WT, including the enrichment of several metabolites, some with potential functional relevance, as well as aroma-active compounds. These findings provide chemical and sensory evidence for the distinctive quality of IT and support further development of this novel specialty tea.