Explicitly modelling field interactions and correlations in complex document structures has recently gained popularity in neural document embedding and retrieval tasks. Although this requires the specification of bespoke task-dependent models, encouraging empirical results are beginning to emerge. We present the first in-depth analyses of non-linear multi-field interaction (NL-MFI) ranking in the cooking domain in this work. Our results show that field-weighted factorisation machines models provide a statistically significant improvement over baselines in recipe retrieval tasks. Additionally, we show that sparsely capturing subsets of field interactions based on domain knowledge and feature selection heuristics offers significant advantages over baselines and exhaustive alternatives. Although field-interaction aware models are more elaborate from an architectural basis, they are often more data-efficient in optimisation and are better suited for explainability due to mirrored document and model factorisation.