Make the corn aioli: Shuck 2 ears yellow corn and cut kernels off cobs. Warm 2 tablespoons olive oil over medium-high heat in a medium skillet. Add corn, season with salt, and saute, stirring occasionally, until softened and just beginning to turn golden in spots, 3 minutes. Add 2 tablespoons water, stirring to remove any bits from the bottom of the pan, and transfer corn to a blender. Let cool completely. (Transfer to refrigerator to speed up the process.)

Meanwhile, prep salad components: Halve 1 ¼ pounds cherry tomatoes and add to a large bowl, along with the drained contents from 1 can large white beans. Squeeze the juice of half a lemon into the tomatoes. Wipe out skillet and return to stovetop over medium-high heat. Add 3 tablespoons olive oil and ½ cup blanched slivered almonds and toast, stirring occasionally, until nuts are golden, 3-4 minutes. Remove from heat and immediately transfer to the bowl with tomatoes and beans, along with 3 more tablespoons olive oil, 2 tablespoons sherry vinegar, and lots of salt and pepper to taste. Set aside until serving, or chill if making in advance.

Finish aioli and serve: Finely grate 1 garlic clove into the blender. Add 3 tablespoons sherry vinegar and the juice of half a lemon, and begin to blend on medium-high. Gradually add ½ cup vegetable oil and the remaining ¼ cup olive oil through the center cap opening, blending until mixture is emulsified and smooth, about 1-2 minutes, depending on the strength of your blender. Season to taste with salt and more sherry vinegar. Toss the chopped herbs through the beans. Plate up, with a big dollop of corn aioli, passing the remainder at the table. Serve with toasted or broiled bread.