Cook bacon in a skillet over medium heat until crisp, 10 to 12 minutes. Transfer to paper towels to drain, and wipe skillet clean.
Butter cut sides of roll or bun. Heat skillet over medium-high heat. Place roll or bun, buttered sides down, in skillet, and cook until golden brown, 1 to 3 minutes.
Mash avocado and blue cheese in a small bowl. Spread mixture on bottom half of roll or bun. Top with tomato and bacon.
Melt butter in skillet over medium heat. Add egg, and cook until white is set, about 1 1/2 minutes. Gently flip egg, and cook until yolk is runny in center but slightly set around edge, about 30 seconds. Remove from pan. Add turkey to pan, and heat through.
Place turkey and egg on top of tomato. Top with remaining half of roll or bun, and serve immediately.