Oeufs en Cocotte

Preheat oven to 250 degrees.

Fit a rimmed baking sheet with a wire rack. Place tomato slices on rack and drizzle with olive oil; season with salt and pepper. Transfer to oven and bake until dry and wrinkled, about 3 hours.

Increase oven temperature to 350 degrees. Brush two 6-ounce ovenproof bowls with butter. Place two slices of tomato in the bottom of each bowl, overlapping slightly. Divide cheese evenly between bowls. Crack 2 eggs into each bowl; season with salt and pepper.

Place bowls on a baking sheet and transfer to oven; bake until yolks are almost set but still slightly runny, 12 to 15 minutes. Remove from oven and preheat broiler.

Spoon 2 teaspoons creme fraiche into each bowl and transfer to broiler. Broil until top is brown and bubbly and whites are set, about 1 minute. Sprinkle with chives and serve immediately.