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Use it anywhere you would use Thai basil or world basil--except traditional Thai food, if that makes sense. I've used basil like that in summer salads (try it with feta and watermelon); I bet it would be lovely in summer grain salads, like the ones recently featured in both Bon Appetit and Fine Cooking. I find the various basils to be very flexible--unless you are making something super traditional, i.e., Thai basil in red curry, holy basil in holy basil stir fry, Italian basil in a fresh mozzarella salad, etc.
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My mind first went in the direction of desserts - I think it would be really nice infused into an ice cream or sorbet. Or perhaps chopped up with some strawberries (and maybe a touch of balsamic)?
I'd also try it in Middle Eastern dishes, which use both aromatics in its spice blends (albeit cinnamon more than basil). It might put an interesting twist on tabbouleh or a tagine, without being too out there.
Or, oooh, cocktails! Sangria, anyone?
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