Slice chicken thighs into 2-inch strips, about 3 to 4 per thigh. Mix together yogurt and remaining ingredients. Pour over the chicken and mix well. Cover, chill and marinate at least 2 hours or overnight.
For the plum compote: Heat a grill pan over medium-high heat and lightly brush the plum halves with oil. Grill, cut side down, for 3 to 4 minutes, or until plums release from the grill with slightly charred grill marks. Remove from the grill and cut into small dice, reserving 1/2 cup of the diced plums for garnish.
In a saucepan, combine the plums and remaining ingredients, and bring to a boil. Reduce heat to medium-low and simmer 30 to 40 minutes, until the plums are broken down and reduced to a jam-like consistency. Add water as necessary if the compote begins to cook dry or burn. Remove the cinnamon stick. If you desire a smoother consistency, puree in a blender or with a stick blender.
For the cashew pesto: Add all ingredients to a blender, with one cup of oil to start. Blend on medium speed until smooth. With the blender running, add remaining oil in a slow stream until a slightly thick paste is formed. Season with salt and pepper as needed.
When ready to grill the chicken, heat a grill pan over medium-high heat. Remove chicken from marinade and wipe away any excess. Thread two pieces of chicken onto each skewer. Lightly brush the pan with oil. Grill the skewers until cooked through, about 4 to 5 minutes per side. Serve with pesto and compote as dipping sauces.