Make the almond-sesame topping: In a medium (10-inch) nonstick skillet over medium-low heat, spread out the almonds in a single layer and toast, stirring frequently, until golden, about 5 minutes. Transfer to a plate and let cool.

Return the pan to the heat and increase the heat to medium. Add the sugar, spreading it in an even layer, and let it melt, without stirring, 1 to 2 minutes. (Watch the pan closely.) Immediately return the almonds to the pan and stir to coat with the sugar. Add the sesame seeds and stir to combine. Immediately transfer the almond mixture to the plate and let cool.

Prepare the halloumi: Rinse out the pan, wipe it dry and return it to medium heat. Add the oil and heat until shimmering. Arrange the halloumi in a single layer in the skillet, leaving a little space between each chunk. Sear until browned on one side, about 2 minutes, then flip the chunks and continue cooking until browned on the other side, about 1 minute more. Transfer to a plate and let cool.

Make the dressing: While the almond mixture and halloumi are cooling, in a medium bowl, whisk together the tahini, water, apple cider vinegar, honey, salt and pepper until smooth and thoroughly combined. You should have about ½ cup.

Make the salad: When the almond-sesame topping is fully cooled, use your hands or a fork to break it apart into bite-size chunks. In a large bowl, toss together the lettuce, radishes, carrot, apple, halloumi, almond-sesame topping and dried cranberries, cherries or raisins, if using, until combined. Drizzle about half of the dressing over the top and toss to coat. Serve immediately, with the rest of the dressing on the side.