In a large bowl, whisk together the 3 tbsp za'atar, 4 garlic cloves, 1 lemon, 1/3 cup extra-virgin olive oil, 1 tsp kosher salt, and 1/2 tsp black pepper. Add 1 1/2 lbs boneless skinless chicken breasts, cut into 1.5-inch cubes and toss to coat every piece thoroughly. Cover and refrigerate for at least 2 hours, ideally overnight.
3 tbsp za'atar, 4 garlic cloves, 1 lemon, 1/3 cup extra-virgin olive oil, 1 tsp kosher salt, 1/2 tsp black pepper, 1 1/2 lbs boneless skinless chicken breasts
Place 1 1/2 lbs mini potatoes in a large pot and cover with cold water. Add a generous amount of salt. Bring to a boil over high heat, then reduce to a simmer and cook for 8–10 minutes, until a paring knife slips into the largest potato with slight resistance, just tender, not falling apart. Drain and let steam dry for 5 minutes.
1 1/2 lbs mini potatoes
In a large bowl, toss the warm potatoes with 3 tbsp extra-virgin olive oil, 1 tsp garlic powder, 1/2 tsp cayenne pepper, 1 tsp smoked paprika, 1 tsp kosher salt, and 1/2 tsp black pepper until evenly coated. Set aside while you prep the aioli.
3 tbsp extra-virgin olive oil, 1 tsp garlic powder, 1/2 tsp cayenne pepper, 1 tsp smoked paprika, 1 tsp kosher salt, 1/2 tsp black pepper
In a medium bowl, whisk together 1/3 cups tahini, 1/3 cups mayonnaise, 4 tbsp lemon juice, 1 garlic clove, 1/2 tsp kosher salt, and 1/2 tsp black pepper whisking until smooth. Slowly stream in 3 tbsp ice-cold water (more as needed), one tablespoon at a time, whisking constantly, until the aioli is silky, creamy, and pourable.
1/3 cups tahini, 1/3 cups mayonnaise, 4 tbsp lemon juice, 1 garlic clove, 3 tbsp ice-cold water, 1/2 tsp kosher salt, 1/2 tsp black pepper
Heat a grill pan over medium-high heat until hot. Remove the chicken from the marinade, letting excess drip off. Working in batches to avoid crowding, grill the chicken for 3–8 minutes per side, until deeply charred and cooked through (internal temp 165°F). Transfer to a plate to rest for 5 minutes.
Wipe the grill pan clean and return to medium-high heat. Add the seasoned potatoes cut-side down in a single layer (work in batches if needed). Grill undisturbed for 4–8 minutes until golden brown and crispy on the cut side.
Thread the grilled chicken and potatoes onto skewers, alternating chicken-potato-chicken-potato. Aim for 3–4 pieces of chicken and 3–4 potato halves per skewer.
Arrange the skewers on a platter. Drizzle generously with the lemon tahini aioli. Garnish with fresh dill and flaky salt.