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1
Peel the plantains. Cut each diagonally at 45 degrees into slices 2 cm thick. The diagonal cut maximises the surface area exposed to heat and is the primary driver of caramelisation.
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2
Place a wide heavy pan over medium heat. Add the oil or butter and allow it to warm until the fat shimmers but does not smoke. Too high a heat will burn the sugars before the interior softens; too low will steam the slices rather than caramelise them. Do not crowd the pan — cook in a single layer with space between each piece. This is where the dish lives or dies: medium heat, uncrowded pan, patience.
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3
If using, scatter the brown sugar into the oil just as the plantains go in. Lay the slices flat and leave them undisturbed. Cook until the underside is deep golden brown — the colour of dark caramel — before turning. This takes several minutes depending on ripeness.
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4
Turn each slice once. Cook the second side until it matches the first: deep golden-brown, visibly caramelised, the flesh yielding and soft at the centre. Transfer to a plate. The slices should be tender through, never firm.