Place the chicken breasts in the slow cooker.
Drizzle the olive oil over the chicken and sprinkle with sea salt, ground black pepper, ground cumin, curry powder, and smoked paprika.
Pour in the coconut cream, 2 tablespoons tahini, the juice of the lemon (reserve 1 teaspoon for the sauce), and the low-sodium chicken broth; stir gently to combine with the chicken and spices.
Cover and cook on high for 3 hours (or on low for 6 hours) until the chicken easily shreds with a fork.
Meanwhile, make the Greek yogurt sauce: whisk together Greek yogurt, 1 teaspoon reserved lemon juice, 1 tablespoon tahini, minced garlic, 1/2 teaspoon ground cumin, and 1/4 teaspoon ground black pepper in a small bowl until smooth.
When the chicken is done, shred it in the slow cooker with two forks or remove and shred on a cutting board, then return to the cooking liquid to keep moist.
Assemble sliders: place a portion of shredded chicken on each slider bun, top with thin cucumber slices, a spoonful of the Greek yogurt sauce, and chopped parsley.