In a large bowl, mix together the turkey, 1 clove of grated garlic, chili powder, paprika, cumin, sumac, egg, salt, and breadcrumbs until very well combined.
Split the turkey into 8 even sections. Form the turkey around 8 skewers, pressing into a long oval shape around the skewer. Place on a parchment-lined sheet tray and store in the refrigerator until ready to grill.
In a blender, blend the feta, yogurt, lemon juice, remaining garlic clove, and olive oil until smooth. The mixture should blend smoothly. If needed, add water 1 tablespoon at a time to thin. Season to taste with salt.
Preheat the grill to 350 F or medium-high heat. Brush the grill with olive oil, then add the kebabs. Cook until browned and charred on each side, about 5 minutes per side.
To serve, remove from the heat and serve with whipped feta sauce.