Cut away the peel and pith from the oranges. Working over a bowl to catch the juice, slice between the membranes to release the segments, then cut those segments in half widthwise. Drain the orange pieces in a fine-mesh strainer, reserving the juice in the bowl below.

Whisk the lemon juice, honey, cumin, cayenne, cinnamon, and salt into the reserved orange juice. Add the grated carrots, the drained oranges, and the juice mixture to a large bowl and toss gently to coat. Let the salad sit for 3 to 5 minutes, until liquid starts to pool in the bottom of the bowl.

Drain the salad in a fine-mesh strainer to remove the excess liquid, then return it to the bowl. Stir in the cilantro and oil, and season with salt and pepper to taste. Serve while the carrots are still crisp and bright.