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To make the marinade, whisk together all ingredients except for turkey in a large bowl. Add turkey and rub the spice mixture all over to coat. Let stand covered for 1 hour at room temperature or for up to 48 hours refrigerated.
- Thread the turkey onto 6 skewers. Rub the grill grates with oil and preheat on medium-high heat for 10 minutes, lighting half the burners but leaving an area where the grill is unlit.
- When grill is hot, add skewers to the direct-heat cooking area.
- Cook until the turkey releases easily from the grates, then flip and cook until nicely grill-marked on all sides. Use oven mitts when flipping as the skewers themselves get very hot.
- Move skewers to unlit part of the grill, close the lid and continue cooking until internal temperature of 165ºF is reached, 8-12 minutes total cooking time.
- To make raita, whisk together all ingredients in a medium bowl. Serve the turkey skewers with the cucumber raita.