Place flour, eggs, and breadcrumbs in three separate and wide shallow bowls.  Working with one eggplant slice at a time, dredge in flour, then dip in egg and then into the breadcrumbs.  Transfer to a wire rack set in a rimmed baking sheet and refrigerate for 30 minutes.  Toss the tomatoes with olive oil and torn basil, and season with salt and pepper.  Heat about 1/4 inch vegetable oil in a large skillet over medium high heat until shimmering.  Add some eggplant slices (don’t overcrowd them) and fry, flipping once until deep golden brown and crunchy (about 2 minutes per side).  Adjusting your heat as necessary.  Remove with a slotted spoon, drain on a clean wire rack set in a rimmed baking sheet, and season with salt and pepper (be generous with your salt!)  Discard your oil and add new oil for frying the remaining eggplant.  Arrange the eggplant and tomatoes on a platter.  Cut the burrata ball in half, place next to the tomatoes and season with salt and pepper.  Scatter the remaining basil on top.