Preheat oven to 400. Arrange prosciutto in a single layer on 2 rimmed baking sheets. Brush with oil, and bake, rotating halfway through, until crisp and deep golden brown, about 9 minutes; transfer to a plate.
Arrange baguette slices on a baking sheet. Brush generously with oil. Bake until light golden brown around edges, 8 to 9 minutes. Rub with garlic cloves.
Mash avocados with a fork. Season with salt and pepper. Spread avocado on baguette slices. Top each with a slice of cheese and a piece of prosciutto. Season with pepper.