For the crab salad:
Remove the top and bottom ends of the tomatoes and strip away any remaining core. Discard ends. Slice tomatoes into 1/2-inch slices, for a total of 12 slices, and set aside. Line a baking sheet with parchment paper and set aside.
To prepare the breading, mix the flour, cayenne, dry mustard, salt, and black pepper in a shallow bowl. Next, whisk the eggs and milk together in a separate bowl. In another shallow bowl, combine the cornmeal and panko. Leave each bowl lined up in the order they were prepared, placing sliced tomatoes at the beginning of the line and prepared parchment-lined pan at the end of the line.
To bread the tomatoes, dredge both sides of one slice in flour mixture, patting off any excess flour. Next, dip the floured slice into the egg wash so it is completely coated. Immediately drop the tomato slice into the cornmeal mixture, turning until evenly coated with breading. Transfer to parchment-lined pan and repeat with remaining slices. Discard any remaining breading ingredients when finished. (The breaded tomatoes can be prepared up to six hours ahead of time. Wrap pan and refrigerate until ready to fry.)
Heat canola oil in a large cast-iron skillet over medium-high heat until hot but not smoking. Cook tomatoes in batches until golden brown all over, two to three minutes per side. Drain on paper towels. (Tomatoes will hold in a single layer in a 200ºF oven until all batches are complete.)
To assemble each stack, place one fried green tomato on individual serving plate. Top with a tablespoon of the crab salad. Top with another fried green tomato, followed by another spoonful of crab salad. Layer the remaining servings in the same fashion, distributing the crab salad evenly. Serve immediately.
Fpr crab salad
Using a sharp knife, scrape the kernels from the ear of corn into a medium bowl. Zest the lime over the corn. Halve the lime and squeeze juice from both halves over the corn. Add chopped cilantro, shallot, the salt and pepper, and olive oil to bowl and stir to combine. Gently fold in lump crabmeat, being careful not to break up big pieces. Cover and refrigerate until ready to assemble, up to six hours in advance.