Preheat the oven to 400 degrees F. Spread the coconut on a nonstick baking sheet and toast in the oven. When the edges start to brown, after about5 minutes, toss the browning pieces around the edges into the center and move the white inside pieces to the outside. Continue to toast until evenly browned, about 1 to 2 minutes more. Transfer to a bowl to cool.
Combine the yogurt and chai spice in a small bowl. Season with a pinch of salt.
Arrange the top rack in your oven so it is as close as possible to the broiler element and preheat the broiler..
Working with one orange at a time, cut 1/4 inch off of the bottom and top of an orange. Stand the fruit cut-side down on a cutting board. Cut off the outer rind and white pith, following the contour of the orange. Turn the orange and slice into 4 even rounds, each about 1/3-inch thick. Repeat with the remaining oranges. Spread the orange slices on a nonstick baking sheet in a single layer. Sprinkle 1/8 teaspoon of sugar evenly over each orange slice and place under the broiler. Cook until the oranges start to turn dark brown, 4 to 5 minutes. Let cool slightly.
Spread the yogurt on a platter; place the orange slices on top and sprinkle with the toasted coconut.
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