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1
Combine the finely shredded bacalhau fibres, smooth mashed potato, beaten egg, grated onion, chopped parsley, nutmeg, and black pepper in a bowl. Work together until the mixture is uniform and stiff — it must hold a firm shape without slumping when scooped. Test by pressing a small amount between two wet spoons: if it sags or runs, the mixture is too wet and will dissolve in the oil.
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2
Using two wet spoons in the quenelle manner, form the mixture into oval shapes approximately 4–5 cm in length, one to two bites each. Transfer to a tray. The formed bolinhos may be refrigerated at this stage for up to 24 hours.
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3
Heat the olive oil in a deep, heavy pan to 170–175 °C. Verify the temperature with a thermometer or by submerging the tip of a wooden spoon — a steady stream of small bubbles confirms readiness. Fry in batches without crowding, turning once, until the exterior is a uniform deep gold.
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4
Lift the bolinhos with a slotted spoon and drain on paper. The crust should be crisp and dry to the touch; the interior, probed at once, should yield and feel hot through. Serve immediately.