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1
Warm the olive oil in a wide, deep pan over a moderate flame. Add the sliced garlic and fry, stirring regularly, until deeply fragrant and beginning to colour at the edges — the oil should smell richly of garlic throughout.
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2
Add the thick bread slices to the pan and fry alongside the garlic, turning once, until each side is golden and the crust is firm. This is where the dish lives or dies: the flavour of the entire soup is built in this pan, in this oil, in these few minutes — underdone bread gives a pale, starchy broth; burnt garlic poisons it.
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3
Remove the pan from the heat entirely. Add the pimentón and stir it through the oil for a few seconds — it must not meet a live flame or it will burn and turn acrid.
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4
Return the pan to the heat. Pour in the water or stock, season aggressively with salt, and bring to a gentle simmer. Cook for 10–15 minutes, stirring occasionally, until the bread has softened and begun to dissolve into the broth, thickening it visibly.
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5
Break one egg per person directly into the simmering soup. Poach for 2–3 minutes until the whites are just set but the yolk remains liquid — the yolk should tremble when the pan is nudged.
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6
Taste the broth and correct the salt — sopa de ajo requires bold seasoning. Ladle into warmed bowls, one egg per bowl, and serve immediately. The yolk is broken into the soup at table.