In a large bowl, whisk together the yogurt, lemon juice, minced garlic, olive oil, paprika, dried mint, and salt to create the marinade.
Add the cubed chicken to the marinade, tossing until well coated. Cover and refrigerate for at least 1 hour to tenderize and flavor the meat.
Thread the marinated chicken cubes onto metal or soaked wooden skewers. Preheat your grill or a grill pan over medium-high heat.
Grill the chicken skewers for 10 to 12 minutes, turning occasionally, until the chicken is beautifully charred and the internal temperature reaches 165 degrees F.
While the chicken grills, melt the butter in a medium saucepan. Add the broken vermicelli and toast for 2 minutes until golden brown.
Stir in the rinsed basmati rice and cook for 1 minute. Pour in the chicken broth, bring to a boil, then reduce heat, cover, and simmer for 15 minutes.
Fluff the rice pilaf with a fork. Serve the warm Shish Tawook skewers over the pilaf, accompanied by garlic sauce, pickled turnips, and a squeeze of fresh lemon.