Peel the onions, halve them crosswise, and slice them thinly.
In a large, heavy-bottomed pot or Dutch oven, melt the butter over low heat.
Add the sliced onions and minced garlic.
Cook slowly, stirring occasionally, for about 1 hour until the onions are deeply soft, sweet, and translucent, but not browned.
Add the vegetable broth to the onions.
Working in batches, carefully transfer the mixture to a blender or food processor and purée until completely smooth.
Pour the smooth onion purée back into the pot.
Stir in the dark beer, cream, salt, paprika, Tabasco, a few grinds of black pepper, sugar, and cider vinegar.
Bring the soup to a gentle simmer over medium-low heat, stirring often, for 20 minutes to allow the flavors to meld.
In a separate medium bowl, whisk the egg yolks until pale and smooth.
While whisking continuously, very slowly pour about one cup of the hot soup into the egg yolks to temper them. This prevents the eggs from scrambling.
Pour the tempered egg yolk mixture back into the main pot of soup, whisking quickly to combine everything.
Continue to cook over very low heat, stirring constantly, for 3 to 5 more minutes until the soup has slightly thickened.
Do not let it boil.
Serve immediately in warm bowls.
Garnish with a sprinkle of hot paprika, or top with toasted croutons and a generous grating of Parmesan cheese.
Patience is key for the onions.
Cook them low and slow for the full hour to develop a deep, sweet, jammy flavor.
Don't be tempted to rush this foundational step!