Adjust racks to middle and top positions and preheat oven to 450 degrees. Wash and dry all produce. Halve sweet potatoes lengthwise; cut crosswise into 1/4-inch-thick half-moons. Toss on a baking sheet with a drizzle of olive oil and a big pinch of salt and pepper. Roast on top rack, flipping halfway through, until tender, 20-25 minutes.

Meanwhile, mince or grate garlic. Halve, peel, and thinly slice shallot. Trim and peel cucumber; grate on the largest holes of a box grater until you have 2 TBSP (4 TBSP for 4 servings). Halve remaining cucumber lengthwise. Scoop out and discard seeds with a spoon; thinly slice crosswise into half-moons. Pick and roughly chop fronds from dill; discard stems.

In a medium bowl, toss together sliced cucumber, half the shallot, vinegar, a drizzle of olive oil, 1/2 tsp sugar (1 tsp sugar for 4 servings), salt, and pepper. In a small bowl, combine sour cream, grated cucumber, half the dill, up to half the garlic (start with a pinch, then taste and add more if desired), 1 tsp water (2 tsp for 4), a drizzle of olive oil, salt, and pepper.

Pat chicken dry with paper towels. Heat a drizzle of olive oil in a large pan over medium-high heat. Add chicken and remaining shallot. Cook, stirring occasionally, until browned, 3-4 minutes. Add remaining garlic and season with Turkish Spice, salt, and pepper. Cook, stirring, until chicken is cooked through, 2-3 minutes. Turn off heat.

Meanwhile, halve pitas to create four pockets (eight pockets for 4 servings). Place on a second baking sheet. When sweet potatoes are almost done roasting, place pitas on middle rack. Toast until warmed through but not crispy, 2-3 minutes.

Fill each pita with chicken, a few sweet potato pieces, tzatziki, and a small amount of cucumber salad. Divide stuffed pitas between plates. Serve remaining cucumber salad and sweet potatoes on the side. Garnish with remaining dill.