To make the compound butter, combine the butter, garlic, chipotle powder, and paprika in a small bowl. Season with salt and pepper to taste. Mix well until evenly combined.
Spread a thin layer of the butter on both sides of the bread slices. Warm a skillet (preferably cast iron) over medium-high heat. Once hot, add the buttered bread to the pan and cook, turning once, until crisp and browned on both sides. (Alternatively, cook on a grill or grill pan.) Remove from the heat and set aside to cool slightly.
Meanwhile, scoop the flesh of the avocados into a medium bowl. Add in the lime juice and salt and mash together coarsely with a fork. Spread a generous layer of the avocado mash on each slice of the toast. Top with some of the hardboiled egg, red onion, tomatoes, and minced cilantro. Serve immediately.