Preheat oven to 375 degrees F. Split sandwich thins; brush cut sides with 2 teaspoons of the olive oil. Place on baking sheet; toast in oven about 5 minutes or until edges are light brown and crisp.
Meanwhile, in a large skillet heat the remaining 2 teaspoons olive oil and the rosemary over medium-high heat. Break eggs, one at a time, into skillet. Cook about 1 minute or until whites are set but yolks are still runny. Break yolks with spatula. Flip eggs; cook on other side until done. Remove from heat.
Place the bottom halves of the toasted sandwich thins on four serving plates. Divide spinach among sandwich thins on plates. Top each with two of the tomato slices, an egg, and 1 tablespoon of the feta cheese. Sprinkle with salt and pepper. Top with the remaining sandwich thin halves.