Heat remaining 1 teaspoon oil in a large nonstick skillet over medium heat. Crack eggs into pan; cook 2 minutes. Cover and cook an additional 2 minutes or until whites are set. Remove from heat.
Combine 1/4 teaspoon salt, ricotta, Parmigiano-Reggiano, and thyme; spread over bread slices. Divide salad and eggs evenly over bread. Sprinkle with remaining 1/8 teaspoon salt and remaining 1/4 teaspoon pepper.