Quarter the pears lengthwise and remove the cores with a paring knife.
Melt the butter in a 10-inch cast-iron skillet over medium-high heat, then stir in 1 tablespoon of the honey and the cinnamon. Turn off the heat and add the pears, turning to coat. Arrange cut-side-down and roast, turning once, until golden and tender, about 30 minutes.
Meanwhile, stir the yogurt, mint, thyme and the remaining 2 tablespoons honey together in a small bowl. Serve the warm pears drizzled with some of the cooking liquid from the skillet, a dollop of the yogurt, and a small mint leaf.