Add the garlic to a small saucepan and coat in olive oil.
Place on your smallest burner and turn the heat on to medium. Once it starts simmering, turn the heat to low and let it go for 20-25 minutes. You want the garlic soft and lightly golden. Let the oil cool.
Add the egg yolks to a baking dish and arrange the garlic cloves around it.
Preheat oven to 180F.
Add the garlic oil over the tops and if needed, add more olive oil on top. Cover with foil.
Add to a larger baking dish and add enough boiling water to cover half of the other dish.
Bake the eggs for 1 hour 15 minutes. Check at the 45 minute mark to see if they're to your liking. Turn oven off and let them sit there for another 15 minutes.
Spread the garlic on the toasted bread, serve the yolk on top, lots of parm, chives, lemon zest and flaky salt.