In a blender, combine the olive oil with fresh basil. Set aside.
In a nonstick pan, on medium heat warm the pastrami on both sides.
In a nonstick pan, heat 1 tbsp oil on medium-high heat. Carefully crack eggs into the pan; Cook until whites are set and around the yolks, about 2 minutes. Season with a pinch salt and pepper.
Toast the bread. Top each with arugula, pastrami, crumbled goat cheese, and eggs. Drizzle with basil oil. Serve with orange sections.