Preheat the oven to 350°F. Lightly grease the bottom and sides of four 4-ounce ramekins with olive oil and place them on a rimmed baking sheet.
Place one salami slice on the bottom of each ramekin, then arrange four more slices around the sides, overlapping. This will be the salami "cup" that holds the eggs.
Break an egg into each "cup."
Bake until the whites are set, about 20 minutes. Gently run a knife around the edges of each cup. Slide a spoon underneath each egg to release it from the ramekin.
Season the cups with salt, pepper, red pepper flakes, and dried parsley. Serve immediately.
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Notes
I typically use large eggs in my recipes. But in this recipe, large eggs might overflow from the cups, so it's best to use medium eggs. Alternatively, you can pour out some of the egg whites before pouring the eggs into the salami shells. To do that, crack each egg into a small bowl, carefully pour out some of the egg white, and then slide the remaining egg into the salami cup.
This is one of those recipes where it's best to make only as many as you think you'll be able to eat right away. However, if you end up with leftovers, you can keep them in the fridge in a sealed container for up to four days. Reheat them covered in the microwave or enjoy them cold. I don't recommend freezing the leftovers.