How to Make It
Bring a large pot of salted water to a boil and fill a large bowl with ice water. Add the corn to the pot and boil for 2 minutes, until glossy. Let cool, then cut the kernels from the cob.
Return the water to a boil and add the lobster. Cook over high heat for 13 minutes, just until the lobster turns red. Immediately plunge the lobster into the ice water to cool. Twist off the tail and claws. Crack the shells and remove the meat. Cut four 1/2-inch-thick slices from the tail and another 4 from a claw and reserve for garnish. Coarsely chop the remaining lobster.
In a medium bowl, using the back of a spoon, mash the garlic to a paste with a pinch of salt. Add the mayonnaise, basil, chives, onion, lemon zest and a generous pinch of pepper. Fold in the chopped lobster and the corn and refrigerate until chilled, about 1 hour.
In a shallow bowl, mix the flour with the smoked paprika and a generous pinch of salt. In another shallow bowl, beat the eggs with the milk and season with salt and pepper. Dredge the green tomato slices in the flour mixture, tapping off the excess. Dip the slices in the egg mixture and then in the flour again.
In a large skillet, heat the oil until shimmering. Add the tomato slices and fry over high heat, turning once, until golden and crisp, about 4 minutes. Drain on paper towels and sprinkle lightly with salt.
Transfer 4 fried tomato slices to plates. Top with the lobster salad and another fried tomato; press lightly to compact the sandwiches. Garnish the knuckle sandwiches with the reserved lobster pieces and serve right away.