Pound the pork chops with a meat mallet or heavy skillet until about 1/4 inch thick; season with salt and pepper. Put the flour in a shallow baking dish. Whisk the eggs, 1/2 teaspoon sesame oil and a pinch each of salt and pepper in a second dish. Put the panko in a third dish. Working with 1 chop at a time, coat in the flour and then dip in the egg, shaking off any excess; firmly press both sides in the panko.
Heat about 1/2 cup vegetable oil in a large nonstick skillet over medium-high heat until very hot (a breadcrumb should instantly sizzle in the oil). Working in batches, fry the chops, turning once, until browned and cooked through, 4 to 5 minutes. Transfer to a paper towel–lined plate to drain; season with salt. (Add more oil to the skillet between batches if needed to maintain a thin layer.)
While the chops cook, whisk the vinegar, miso, 2 teaspoons vegetable oil and the remaining 1 1/2 teaspoons sesame oil in a large bowl until smooth. Add the greens, carrots and tomatoes and toss; season with salt and pepper. Serve with the pork chops.