Heat oil in a large skillet over medium-high heat. Fry two tortillas at a time until firm, but not crisp, about 30 seconds per side. Drain on paper towels.

Reduce heat to medium and add more oil if needed. Crack in eggs and cook until edges are opaque, about 1 minute. Cover, reduce heat to low, and cook until whites are set, about 4 minutes.

Combine refried beans and butter in a microwave-safe dish. Cover and microwave on high in 1-minute intervals until hot.