Making the prosciutto cups: Line 12 mini-muffin cups with the halved prosciutto slices.
Making the spinach: Heat the olive oil in a large saute pan and cook the garlic over medium-high heat until golden, about 30 seconds. Add the spinach and saute, stirring continuously until the spinach just begins to brown, 2 to 3 minutes. Remove from the heat and let cool slightly.
Bake the cups until the eggs are cooked and the prosciutto is crispy, about 10 minutes. Serve warm.