In a saucepan, add the chicken thighs and enough water to cover the meat. Bring to a boil and cook the chicken for approximately ten minutes, or until the internal temperature reaches 165°F (74°C).
Remove the chicken from the saucepan and let it cool slightly. Cut the meat into bite-sized pieces or shred it, depending on your preference. Set aside.
Whisk together garlic, sesame paste, water, soy sauce, rice vinegar, sugar, Sichuan pepper powder, and chili oil in a small bowl. Adjust the amount of chili oil to your desired level of spiciness. Set aside.
On a serving dish, arrange a bed of shredded cucumbers at the bottom. Place the cooked chicken pieces on top of the cucumbers. Generously pour the prepared sauce over the chicken, ensuring it is evenly coated. Optionally, garnish with chopped green onions or cilantro for added freshness and visual appeal.