Start by pickling the veggies. They only need to sit in the brine for 20 to 30 minutes, but you can make them up to a week in advance and keep them in a sealed jar in the fridge if desired. Thinly slice or shave the fennel and red onion, using a mandolin (my preference) or sharp knife. Combine the apple cider vinegar, water, sugar, and salt in a saucepan. Cook over medium heat for about 3 to 5 minutes, stirring frequently, until heated to a gentle simmer and the sugar and salt dissolve. You can also use very hot water from your tap to accomplish the same thing if you don't want to do the extra step of heating the brine. Put the sliced fennel and onion in a bowl. Pour the brine over the veggies and let them sit at room temp.
Next, prep the chicken if you haven't already cooked it and aren't using pre-made or rotisserie chicken. I prefer to the boil the chicken breasts. Place them in a large pot, cover with water or broth (enough so they're covered by an inch), and bring to a boil. Cover the pot, reduce heat to maintain a simmer, and cook until the chicken reaches an internal temperature of 165℉/74℃. Remove the chicken from the pot and shred it with two forks (or let it cool and use your hands).
While the chicken is cooking, gather the other ingredients and prepare the dressing. In a bowl or measuring cup, stir together the Greek yogurt, olive oil, lemon juice, garlic, salt, and pepper.
At this point, the veggies should be done pickling. Remove them from the brine with a slotted spoon or fork. Discard the brine.
Combine the pickled fennel and onion, shredded chicken, dried cherries, sliced almonds, capers, and fennel fronds in a large bowl.
Pour the dressing over the salad ingredients. Stir until coated. Taste and adjust seasonings as desired.
Enjoy right away or after chilling in the fridge for an hour!
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