Prep: 1. Preheat oven to 400. 2. Cut each slice of bread into 4 long batons (each should be about the size of your index finger). 3. Grate cheese. Make: 1. Place batons on a baking sheet in an even layer and bake in oven, turning bread every so often, until dry and golden brown, 5-10 minutes. 2. Remove baking sheet from oven, and drizzle oil evenly over toasts. 3. Scatter over grated cheese and thyme leaves to top each toast. 4. Wrap each toast with a strip of prosciutto and then place toasts back on baking sheet, being sure to leave a bit of space between them. 5. Return baking sheet to oven and bake toasts until prosciutto is just barely beginning to crisp, 5-10 minutes. 6. Meanwhile, boil a pot of water. Gently add eggs to water and cook for exactly 3 minutes. 7. Using a slotted spoon, transfer eggs to bowls or individual egg cups. Serve eggs with toasts. To eat, use a table knife to cut top off of each egg and use a little spoon to dig out the beautifully cooked egg, spreading yolk on savory toast, or even dipping your toast into the egg yolk.