1. The day before, soak the split peas in a large bowl.
2. On the day of the recipe, peel and chop the garlic.
Rinse the split peas, drain them, and put them in a saucepan.
Add water (two and a half times the volume of the split peas) and the chopped garlic.
Mix for a few moments, then cover and simmer for 20 minutes, stirring occasionally.
3. Heat water in a small saucepan.
When it simmers, gently lower the egg using a tablespoon.
Let it cook for 5 minutes and 30 seconds if it is small and 6 minutes if it is large.
When it is ready, transfer it to a bowl of cold water to stop the cooking process.
Tap it on the table to crack the shell, then delicately remove it.
4. Pour olive oil into a hot skillet, add a little salt and pepper, and let it brown for a few seconds while stirring.
5. When the split peas are almost melting in the mouth, drain them over a saucepan to keep the liquid. Puree them with an immersion blender gradually until you have a smooth texture, neither too liquid nor too thick; if necessary, adjust with a little of the reserved cooking water.
Season with salt and pepper. Put the puree in a bowl, add the soft-boiled egg on top.