Heat a grill pan or grill to medium heat.
Cut kernels from 1 corn cob and toss with toasted bread, shallot, chile, white balsamic vinegar, and lime juice in a large bowl; season with salt and pepper and set aside.
Combine tomatoes with 2 tablespoons of the oil and season with salt and pepper then set aside until ready to use.
Meanwhile, brush remaining ear of corn with some oil and grill, turning occasionally, until tender and charred in spots, about 8 to 10 minutes.
Set corn aside until cool enough to handle then cut kernels from cobs. Cut off the cooled kernels and add to reserved corn mixture along with avocado, cheese, cilantro, greens and remaining 2 tablespoons of oil.
Toss to combine, season with salt and pepper, taste, and adjust flavors as desired. Serve immediately.