For any of the three recipes, prepare cucumber by using a vegetable peeler or knife to partially skin the cucumber with vertical stripes. Scoop out the seeds with a spoon. Cut the cucumber in half vertically. For the hot-and-sour cucumbers, use a mandolin or sharp knife to cut the cucumber halves into 1/8-inch slices. For the mala or sesame cucumbers, smack the two cucumber pieces along the back with a heavy knife or rolling pin until they start to break down a bit and the skin starts to crack. Cut in half again vertically and then diagonally into bite-size pieces.
Put slices or pieces in a colander and mix well with 1 teaspoon kosher salt. Let sit and drain for 30 minutes. Pat the cucumbers dry with a clean towel or paper towel and transfer to a bowl.
For the hot-and-sour cucumbers, add the sliced fresh or pickled chilies to the cucumbers. Mix the rice vinegar, water and sugar together and pour over the cucumbers and chilies.
For the mala cucumbers, add the 1 teaspoon vinegar to the cucumbers. In a small sauce pan or wok, heat the oil over medium heat until slightly hot and a test Sichuan peppercorn starts to sizzle. Add the peppercorns and cook until they sizzle and smell very fragrant. Add the dried chili peppers and toss quickly, allowing them to get toasty but not burned. Immediately pour the oil and peppers over the cucumbers and mix well.
For the sesame cucumbers, mix the yacai, sesame paste, vinegar, sesame oil and garlic together well in a small bowl. Combine with the cucumbers and mix well. Drizzle the cucumbers with the chili oil and its crisp.