Chicago chef Stephanie Izard makes the ultimate summer salad with a creamy version of sweet-salty Japanese unagi sauce, which is typically brushed over eel. Slideshow: More Tomato Recipes
In a small saucepan, combine the soy sauce with the mirin, sugar and soju; bring to a boil. Simmer over moderate heat, stirring, until reduced to 1/4 cup, about 12 minutes. Let cool completely, then whisk in the mayonnaise and lime juice and season with salt.
Light a grill or preheat a grill pan. Brush the green tomatoes with oil and season with salt. Grill over high heat, turning once, until lightly charred, 4 minutes. Transfer to a plate to cool, then cut into quarters.
In a perforated grill pan, toss the whole grape tomatoes with the 1 tablespoon of oil and season with salt. Grill over high heat, tossing occasionally, until lightly charred, about 2 minutes. Let cool slightly.
On a platter, toss the mozzarella with all of the tomatoes. Drizzle 1/2 cup of the unagi sauce over the salad and scatter the basil and mint on top. Serve, passing the remaining sauce at the table.
The unagi sauce can be refrigerated for up to 3 days. Bring to room temperature before serving.
Pair this umami-rich salad with a dry ale.