Bring a large pot of salted water to a boil. Plunge the spigarello into the boiling water for 2-3 minutes.
Meanwhile, heat the olive oil in a saute pan over medium heat and then add in the garlic, cooking until fragrant, about 30 seconds.
With tongs or a slotted spoon, remove the spigarello from the boiling water and put it in the saute pan, tossing to coat. Saute for about 3-4 minutes.
Meanwhile, turn the heat on the cooking water down to low. When the boiling dies down, swirl the water in the pot gently and slip the eggs into the middle of the whirlpool. Cook the eggs for 5-6 minutes (or however done you like them).
When the eggs are done, remove them from the water with a slotted spoon and transfer them to a folded paper towel to soak up any water.
Plate the spigarello with the eggs on top. Sprinkle with extra salt and pepper and serve immediately.