My short answer is have participants repeatedly taste and choose between recipes in a "2-interval forced choice paradigm" followed by logistic regression, using ingredients to predict probability of recipe choice.
In terms of the main experimental structure, we probably want each participant to do a number of two-interval forced-choice trials (2IFC, as they're called -- closely related to the 2AFC, or 2-alternative forced-choice) in which they taste two recipes in sequence (with an appropriate palette cleanser in between) and pick one. We want to give them all pairings of candidate recipes multiple times and balance the order of exposure within trials. In a perfect world, the experiment would be about as many minutes and spoonfuls as a meal, so that any effects of time (heat building or desensitization) remain with the normal range for a meal. But obviously there is a trade off with wanting to get more data.
Much of the difficulty with this sort of research is getting people to give good data. We probably need to screen out smokers, anyone recovering from a cold, and anyone else who might have decreased taste acuity. After we get our data, we will want to exclude particularly inconsistent participants using some predefined criterion. Similarly, people who show an unusual effect of within-trial stimulus order (preferring, say, the first over the second in each comparison) might also be given the hairy eyeball. Ideally we'd run a screening session at the start of the experiment and only advance people who give good data to our real tests.
There will still be potential issues with participants learning to discriminate or changing preference across trials (especially if the heat builds up or they desensitize to it). We may be able minimize this with our screening session or by using people with presumed stable preference as participants, such as experienced chili cooks. (Though we should ask ourselves what larger population we're trying to study. If we want to sell spice mixes maybe it is cooks; if we want to sell chili in a restaurant then we probably shouldn't just study cooks). No matter what, we will still probably want to exclude the first few trials from analysis as "practice trials" because they're always weird.
For our main analysis, I might do a logistic regression predicting their probability of recipe preference using trial (grouping trials in some reasonable quantile like 4ths) and ingredient levels (and interactions) as fixed effects.
One can imagine also needing a total heat random effect that might vary by participant. Or we could determine each participants' preferred Scoville units in screening and keep it constant.
Generally, the relationship between a physical stimulus and its perceived intensity isn't linear and is often said to be exponential (Stevens power law). So we may end up transforming our ingredient amount variables.
Finally, experience tells us that we seldom run a first experiment that perfectly answers the right question. And it may turn out that the real question isn't preferred spicing of chili in the context of other chili recipes, but preference in the context of a meal. And our design is unable to assess most potential adverse effects. And we're not dealing with the fact that natural products vary in their chemical constituents and flavors. But you have to start somewhere.
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Chapman, K. W., K. GRACE‐MARTIN, and H. T. Lawless. "Expectations and stability of preference choice." Journal of sensory studies 21.4 (2006): 441-455.
Karrer, T., and L. Bartoshuk. "Capsaicin desensitization and recovery on the human tongue." Physiology & behavior 49.4 (1991): 757.
Lawless, Harry T., and Hildegarde Heymann. "Physiological and psychological foundations of sensory function." Sensory Evaluation of Food (2010): 19-56.