Place your cucumbers, cut side down, into a large plastic or reusable ziploc bag (to prevent splatter). Use a rolling pin to smash the cucumber into pieces (put some muscle into it!). Tear remaining large chunks into pieces. Alternatively, just chop it into bite-sized pieces. Transfer to a large bowl. Add the avocado, red onion (if using), vinegar, soy sauce, sesame oil, 1 tablespoon olive oil, and ½ teaspoon salt. Toss to coat. Set aside to marinate.
Place a piece of parchment on top of your cutting board. Place the chicken cutlets on top. Place another piece of parchment over top. Use a rolling pin to pound the chicken until it’s about ¼-inch thick (also requires some muscle). Season each side of the chicken generously with salt and pepper (about ¼ tsp salt per cutlet). Drizzle olive oil onto each side and rub it around to coat the chicken.
Heat a large skillet over medium-high heat. Once the pan is hot, add the chicken cutlets to the pan and cook for about 3-5 minutes, or until browned and mostly cooked through. Flip over and cook for another 2 minutes, or until cooked through. Transfer to a plate. If you weren’t able to fit all of your cutlets onto the pan, carefully wipe out the skillet to get any burnt browned bits off. Repeat with any remaining cutlets and transfer to a plate. Don’t wipe out the skillet once all the chicken is cooked.
Add tomatoes, ¼ cup water, and ¼ tsp salt to the hot pan and cook, stirring occasionally and scraping up any brown bits, until the tomatoes start to burst open, about 3 minutes. If the pan starts looking dry, just add some more water.
Serve the chicken cutlets with burst tomatoes and top with cucumber avocado salad, cilantro, and a drizzle of the dressing that’s pooled at the bottom of the bowl.