Preheat the oven to 350°F.
Whisk the eggs together in a medium bowl. Add the cinnamon, sugar, and honey to the bowl. Stir until combined.
Heat the olive oil in a medium cast-iron skillet over medium-high heat. Add the eggs to the pan and cook for 4 minutes. Arrange the peaches over the top and sprinkle with the thyme and goat cheese. Place in the oven and bake for 20 to 25 minutes. Remove from the oven.
Slice into wedges and serve immediately.