Prepare all ingredients as listed.
Boil water for green tea. Once boiling, remove from heat and allow to cool slightly. Steep the green tea for two to three minutes, then remove tea bags or strain.
Toast sourdough bread until golden. Spread with butter.
Heat a large nonstick skillet over medium low heat and add butter.
Crack eggs into the pan in batches if needed, keeping yolks intact. Season lightly with salt and black pepper. Cook gently until whites are fully set and yolks remain runny, about four to five minutes. Cover briefly if needed to set the tops without flipping.
Toss arugula with olive oil, lemon juice, salt, and black pepper. Divide between two plates.
Serve the eggs with arugula, bread, fruit, and green tea.