Place potato on a microwave-safe plate; pierce 3 or 4 times with a fork. Cook in the microwave for 5 minutes. Flip using the fork. Cook for 3 minutes more. Cool potato slightly, about 3 minutes. Cut in halve lengthwise.
Spread butter evenly over the potato halves. Top each half with a slice of American cheese and Cheddar cheese.
Heat a nonstick skillet over medium-high heat. Break eggs and slide gently into the skillet one at a time. Reduce heat to low; cook eggs until whites are firm and yolks begin to thicken, about 2 minutes. Flip and continue cooking until yolks thicken to desired doneness, 2 to 3 minutes more.
Place one egg over each potato half; garnish with green onion and sriracha sauce.